Basic Technical Mathematics With Calculus SI Version Canadian 10th Edition By Washington - Test Bank

Basic Technical Mathematics With Calculus SI Version Canadian 10th Edition By Washington – Test Bank

 

Instant Download – Complete Test Bank With Answers

 

 

Sample Questions Are Posted Below

 

Basic Technical Mathematics with Calculus, 10e (Washington)

Chapter 5   Systems of Linear Equations; Determinants

 

5.1   Linear Equations

 

1   Determine if Pair of Values is Solution of Equation

 

Determine whether or not the ordered pair is a solution of the linear equation.

 

1) x + y = 13; (7, 6)

1. A) Yes
2. B) No

Answer:  A

Type: BI     Var: 48

Topic:  5.1 Linear Equations

Skill:  Recall

Objective:  (5.1) Determine if Pair of Values is Solution of Equation

 

2) x + y = 12; (6, 7)

1. A) Yes
2. B) No

Answer:  B

Type: BI     Var: 41

Topic:  5.1 Linear Equations

Skill:  Recall

Objective:  (5.1) Determine if Pair of Values is Solution of Equation

 

3) x – y = 25; (5, 2)

1. A) Yes
2. B) No

Answer:  B

Type: BI     Var: 41

Topic:  5.1 Linear Equations

Skill:  Recall

Objective:  (5.1) Determine if Pair of Values is Solution of Equation

 

4) 4x + y = 12; (2, 4)

1. A) Yes
2. B) No

Answer:  A

Type: BI     Var: 50+

Topic:  5.1 Linear Equations

Skill:  Recall

Objective:  (5.1) Determine if Pair of Values is Solution of Equation

 

 

5) 5x + 4y = 36; (4, 4)

1. A) Yes
2. B) No

Answer:  A

Type: BI     Var: 50+

Topic:  5.1 Linear Equations

Skill:  Recall

Objective:  (5.1) Determine if Pair of Values is Solution of Equation

6) 3x – 2y = 16; (4, 2)

1. A) Yes
2. B) No

Answer:  B

Type: BI     Var: 50+

Topic:  5.1 Linear Equations

Skill:  Recall

Objective:  (5.1) Determine if Pair of Values is Solution of Equation

 

7) -5x – 11y = -38; (1, 3)

1. A) Yes
2. B) No

Answer:  A

Type: BI     Var: 50+

Topic:  5.1 Linear Equations

Skill:  Recall

Objective:  (5.1) Determine if Pair of Values is Solution of Equation

 

8) y = -2x; (-1, 2)

1. A) Yes
2. B) No

Answer:  A

Type: BI     Var: 24

Topic:  5.1 Linear Equations

Skill:  Recall

Objective:  (5.1) Determine if Pair of Values is Solution of Equation

 

9) y = -3; (-1, 5)

1. A) Yes
2. B) No

Answer:  B

Type: BI     Var: 47

Topic:  5.1 Linear Equations

Skill:  Recall

Objective:  (5.1) Determine if Pair of Values is Solution of Equation

 

 

10) x + 8 = 0; (-8,4)

1. A) Yes
2. B) No

Answer:  A

Type: BI     Var: 50+

Topic:  5.1 Linear Equations

Skill:  Recall

Objective:  (5.1) Determine if Pair of Values is Solution of Equation

2   Find Solution of Equation Given One Value

 

For the given value of x, determine the value of y that gives a solution to the given linear equation in two unknowns.

 

1) -3x + 8y = -33; x = 2

1. A) –
2. B)
3. C)
4. D) –

Answer:  A

Type: BI     Var: 50+

Topic:  5.1 Linear Equations

Skill:  Recall

Objective:  (5.1) Find Solution of Equation Given One Value

 

2) 4x – 3y = -7; x =

1. A)
2. B) –
3. C) –
4. D)

Answer:  D

Type: BI     Var: 50+

Topic:  5.1 Linear Equations

Skill:  Recall

Objective:  (5.1) Find Solution of Equation Given One Value

 

 

3) 3.6y + 1x = 18.4; x = 0.4

5. A) -5.0
6. B) 5.0
7. C) 0.6
8. D) 0.4

Answer:  B

Type: BI     Var: 50+

Topic:  5.1 Linear Equations

Skill:  Recall

Objective:  (5.1) Find Solution of Equation Given One Value

3   Determine if Pair of Values is Solution of System

 

Determine whether or not the given pair of values is a solution of the given system.

 

1) x = 1, y = 3

 

x + y = 4

x – y = -2

 

1. A) Yes
2. B) No

Answer:  A

Type: BI     Var: 50+

Topic:  5.1 Linear Equations

Skill:  Recall

Objective:  (5.1) Determine if Pair of Values is Solution of System

 

2) x = -3, y = -2

 

x + y = 1

x – y = 5

 

1. A) Yes
2. B) No

Answer:  B

Type: BI     Var: 50+

Topic:  5.1 Linear Equations

Skill:  Recall

Objective:  (5.1) Determine if Pair of Values is Solution of System

 

 

3) x = 5, y = -6

 

3x + y = 9

4x + 3y = 2

 

1. A) Yes
2. B) No

Answer:  A

Type: BI     Var: 50+

Topic:  5.1 Linear Equations

Skill:  Recall

Objective:  (5.1) Determine if Pair of Values is Solution of System

4) x = 2, y = 1

 

2x + y = 3

3x + 2y = 4

 

1. A) Yes
2. B) No

Answer:  B

Type: BI     Var: 50+

Topic:  5.1 Linear Equations

Skill:  Recall

Objective:  (5.1) Determine if Pair of Values is Solution of System

 

5) x = -0.5, y = 0.2

 

 

1. A) Yes
2. B) No

Answer:  A

Type: BI     Var: 50+

Topic:  5.1 Linear Equations

Skill:  Recall

Objective:  (5.1) Determine if Pair of Values is Solution of System

 

 

6) x = -0.3, y = 0.4

 

 

1. A) Yes
2. B) No

Answer:  B

Type: BI     Var: 50+

Topic:  5.1 Linear Equations

Skill:  Recall

Objective:  (5.1) Determine if Pair of Values is Solution of System

4   Solve Apps: Determine if Pair of Values is Solution of System

 

Answer the question.

 

1) Forces, measured in newtons, on a beam produce the following equilibrium equations:

 

 

 

Are the reaction forces R1 = 1480 N and R2 = 3055 N?

1. A) Yes
2. B) No
3. C) Cannot be determined

Answer:  A

Type: BI     Var: 50+

Topic:  5.1 Linear Equations

Skill:  Applied

Objective:  (5.1) Solve Apps: Determine if Pair of Values is Solution of System

 

2) Forces, measured in newtons, on a beam produce the following equilibrium equations:

 

 

 

Are the reaction forces = 3095 N and  = 1500 N?

1. A) Yes
2. B) No
3. C) Cannot be determined

Answer:  B

Type: BI     Var: 50+

Topic:  5.1 Linear Equations

Skill:  Applied

Objective:  (5.1) Solve Apps: Determine if Pair of Values is Solution of System

 

3) The equations for a circuit are:

 

 

where the currents are measured in amperes. Are the currents  = 2.5 A and

1. A) Yes
2. B) No
3. C) Cannot be determined

Answer:  B

Type: BI     Var: 50+

Topic:  5.1 Linear Equations

Skill:  Applied

Objective:  (5.1) Solve Apps: Determine if Pair of Values is Solution of System

4) Supply and demand equations are given by:

 

 

where y represents price in dollars and x represents the number of items in supply.  The market equilibrium is the solution to this system. At market equilibrium, is the supply 9 items and the price $1170?

1. A) Yes
2. B) No
3. C) Cannot be determined

Answer:  A

Type: BI     Var: 50+

Topic:  5.1 Linear Equations

Skill:  Applied

Objective:  (5.1) Solve Apps: Determine if Pair of Values is Solution of System

 

 

5) Supply and demand equations are given by:

 

 

where y represents price in dollars and x represents the number of items in supply.  The market equilibrium is the solution to this system. At market equilibrium, is the supply 21 items and the price $880?

1. A) Yes
2. B) No
3. C) Cannot be determined

Answer:  B

Type: BI     Var: 50+

Topic:  5.1 Linear Equations

Skill:  Applied

Objective:  (5.1) Solve Apps: Determine if Pair of Values is Solution of System

 

5.2   Graphs of Linear Functions

 

1   Find Slope of Line Given Points

 

Find the slope of the line that passes through the given points.

 

1) (8, -2), (5, 4)

1. A) 3
2. B) 6
3. C) 2
4. D) -2

Answer:  D

Type: BI     Var: 50+

Topic:  5.2 Graphs of Linear Functions

Skill:  Recall

Objective:  (5.2) Find Slope of Line Given Points

2) (-2, -3), (5, 9)

1. A) 6
2. B)
3. C)
4. D) Undefined

Answer:  B

Type: BI     Var: 50+

Topic:  5.2 Graphs of Linear Functions

Skill:  Recall

Objective:  (5.2) Find Slope of Line Given Points

 

3) (-9, -2), (-7, 6)

1. A) 2
2. B) 8
3. C) 4
4. D) Undefined

Answer:  C

Type: BI     Var: 50+

Topic:  5.2 Graphs of Linear Functions

Skill:  Recall

Objective:  (5.2) Find Slope of Line Given Points

 

4) (-3, -9), (2, -2)

1. A)
2. B) 1
3. C) –
4. D) Undefined

Answer:  A

Type: BI     Var: 50+

Topic:  5.2 Graphs of Linear Functions

Skill:  Recall

Objective:  (5.2) Find Slope of Line Given Points

 

5) (-1, 6), (7, 6)

1. A) 15
2. B) 7
3. C) 0
4. D) 1

Answer:  C

Type: BI     Var: 50+

Topic:  5.2 Graphs of Linear Functions

Skill:  Recall

Objective:  (5.2) Find Slope of Line Given Points

 

2   Sketch Line Given Slope, y-Intercept

 

Sketch the line with the given slope and y-intercept.

 

1) m = , (0, 3)

 

1. A)
2. B)

 

1. C)
2. D)

Answer:  D

Type: BI     Var: 25

Topic:  5.2 Graphs of Linear Functions

Skill:  Applied

Objective:  (5.2) Sketch Line Given Slope, y-Intercept

 

 

2) m = – 5, (0, 5)

 

1. A)
2. B)

 

1. C)
2. D)

Answer:  D

Type: BI     Var: 50+

Topic:  5.2 Graphs of Linear Functions

Skill:  Applied

Objective:  (5.2) Sketch Line Given Slope, y-Intercept

 

 

3) m = – , (0, 4)

 

1. A)
2. B)
3. C)

 

1. D)

Answer:  A

Type: BI     Var: 50+

Topic:  5.2 Graphs of Linear Functions

Skill:  Applied

Objective:  (5.2) Sketch Line Given Slope, y-Intercept

 

 

4) m = 0.6, (0, -0.8)

 

 

1. A)
2. B)

 

1. C)
2. D)

Answer:  D

Type: BI     Var: 50+

Topic:  5.2 Graphs of Linear Functions

Skill:  Applied

Objective:  (5.2) Sketch Line Given Slope, y-Intercept

 

5) m = , (0, 3)

 

1. A)
2. B)

 

1. C)
2. D)

Answer:  B

Type: BI     Var: 50+

Topic:  5.2 Graphs of Linear Functions

Skill:  Applied

Objective:  (5.2) Sketch Line Given Slope, y-Intercept

 

 

3   Find Slope, y-Intercept

 

Find the slope and the y-intercept of the line with the given equation.

 

1) y = x – 3

1. A) Slope: – ; y-intercept: (0, 3)
2. B) Slope: ; y-intercept: (0, -3)
3. C) Slope: – ; y-intercept: (0, -3)
4. D) Slope: ; y-intercept: (0, 3)

Answer:  B

Type: BI     Var: 12

Topic:  5.2 Graphs of Linear Functions

Skill:  Recall

Objective:  (5.2) Find Slope, y-Intercept

2) 4x + 3y = 31

1. A) Slope: ; y-intercept (0, )
2. B) Slope: – ; y-intercept: (0, )
3. C) Slope: – ; y-intercept: (0, )
4. D) Slope: ; y-intercept: (0, )

Answer:  C

Type: BI     Var: 50+

Topic:  5.2 Graphs of Linear Functions

Skill:  Recall

Objective:  (5.2) Find Slope, y-Intercept

 

 

3) 2x + 7y = 34

1. A) Slope: ; y-intercept: (0, )
2. B) Slope: 3; y-intercept: (0, )
3. C) Slope: -3; y-intercept: (0, )
4. D) Slope: – ; y-intercept: (0, )

Answer:  D

Type: BI     Var: 50+

Topic:  5.2 Graphs of Linear Functions

Skill:  Recall

Objective:  (5.2) Find Slope, y-Intercept

 

4) -4x + 8y = 16

1. A) Slope: – ; y-intercept: (0, -2)
2. B) Slope: ; y-intercept: (0, 2)
3. C) Slope: 2; y-intercept: (0, -2)
4. D) Slope: -2; y-intercept: (0, 2)

Answer:  B

Type: BI     Var: 50+

Topic:  5.2 Graphs of Linear Functions

Skill:  Recall

Objective:  (5.2) Find Slope, y-Intercept

5) -3x + 4y = -4

1. A) Slope: – ; y-intercept: (0, 1)
2. B) Slope: ; y-intercept: (0, -1)
3. C) Slope: -1; y-intercept: (0, -1)
4. D) Slope: 1; y-intercept: (0, 1)

Answer:  B

Type: BI     Var: 24

Topic:  5.2 Graphs of Linear Functions

Skill:  Recall

Objective:  (5.2) Find Slope, y-Intercept

 

4   Sketch Graph

 

Sketch the graph of the line with the given equation.

 

1) y = 4x – 4

 

1. A)
2. B)

 

1. C)
2. D)

Answer:  D

Type: BI     Var: 18

Topic:  5.2 Graphs of Linear Functions

Skill:  Applied

Objective:  (5.2) Sketch Graph

 

 

2) -2y = x – 2

 

1. A)
2. B)

 

1. C)
2. D)

Answer:  B

Type: BI     Var: 50+

Topic:  5.2 Graphs of Linear Functions

Skill:  Applied

Objective:  (5.2) Sketch Graph

 

 

3) 28y = 4x – 20

 

1. A)
2. B)

 

1. C)
2. D)

Answer:  C

Type: BI     Var: 50+

Topic:  5.2 Graphs of Linear Functions

Skill:  Applied

Objective:  (5.2) Sketch Graph

 

 

4) 4y + 16x = -28

 

1. A)
2. B)

 

1. C)
2. D)

Answer:  D

Type: BI     Var: 50+

Topic:  5.2 Graphs of Linear Functions

Skill:  Applied

Objective:  (5.2) Sketch Graph

 

 

5) -3x – 12y = 9

 

1. A)
2. B)

 

1. C)
2. D)

Answer:  C

Type: BI     Var: 50+

Topic:  5.2 Graphs of Linear Functions

Skill:  Applied

Objective:  (5.2) Sketch Graph

 

 

6) -3x + 4y = -12

 

1. A)
2. B)

 

1. C)
2. D)

Answer:  A

Type: BI     Var: 50+

Topic:  5.2 Graphs of Linear Functions

Skill:  Applied

Objective:  (5.2) Sketch Graph

 

 

7) 6x – y = 0

 

1. A)
2. B)

 

1. C)
2. D)

Answer:  C

Type: BI     Var: 16

Topic:  5.2 Graphs of Linear Functions

Skill:  Applied

Objective:  (5.2) Sketch Graph

 

 

8) 7x + y = 0

 

1. A)
2. B)

 

1. C)
2. D)

Answer:  C

Type: BI     Var: 16

Topic:  5.2 Graphs of Linear Functions

Skill:  Applied

Objective:  (5.2) Sketch Graph

 

 

9) y + 2 = 0

 

1. A)
2. B)

 

1. C)
2. D)

Answer:  B

Type: BI     Var: 4

Topic:  5.2 Graphs of Linear Functions

Skill:  Applied

Objective:  (5.2) Sketch Graph

 

 

5   Find x, y-intercepts

 

Find the intercepts for the equation.

 

1) x + y = 5

1. A) (0, 3) (0, 2)
2. B) (5, 2) (3, 5)
3. C) (5, 0) (0, 5)
4. D) (3, 0) (2, 0)

Answer:  C

Type: BI     Var: 4

Topic:  5.2 Graphs of Linear Functions

Skill:  Recall

Objective:  (5.2) Find x, y-intercepts

2) x + y = -1

1. A) (0, -5) (0, 4)
2. B) (-5, 0) (4, 0)
3. C) (-1, 0) (0, -1)
4. D) (-1, 4) (-5, -1)

Answer:  C

Type: BI     Var: 4

Topic:  5.2 Graphs of Linear Functions

Skill:  Recall

Objective:  (5.2) Find x, y-intercepts

 

3) x + y = -1

1. A) (0, -2) (0, 1)
2. B) (-2, 0) (1, 0)
3. C) (-1, 1) (-2, -1)
4. D) (-1, 0) (0, -1)

Answer:  D

Type: BI     Var: 24

Topic:  5.2 Graphs of Linear Functions

Skill:  Recall

Objective:  (5.2) Find x, y-intercepts

 

4) 3x + y = 3

1. A) (4, 0) (-9, 0)
2. B) (3, -9) (4, 3)
3. C) (1, 0) (0, 3)
4. D) (0, 4) (0, -9)

Answer:  C

Type: BI     Var: 50+

Topic:  5.2 Graphs of Linear Functions

Skill:  Recall

Objective:  (5.2) Find x, y-intercepts

 

5) 2x + y = 0

1. A) (0, -2) (0, 4)
2. B) (-2, 0) (4, 0)
3. C) (0, 4) (-2, 0)
4. D) (0, 0) (0, 0)

Answer:  D

Type: BI     Var: 50+

Topic:  5.2 Graphs of Linear Functions

Skill:  Recall

Objective:  (5.2) Find x, y-intercepts

6) -2x + y = 4

1. A) (-2, 0) (0, 4)
2. B) (0, -1) (0, 2)
3. C) (4, 2) (-1, 4)
4. D) (-1, 0) (2, 0)

Answer:  A

Type: BI     Var: 50+

Topic:  5.2 Graphs of Linear Functions

Skill:  Recall

Objective:  (5.2) Find x, y-intercepts

 

7) -2x + 2y = 8

1. A) (-7, 0) (-6, 0)
2. B) (-4, 0) (0, 4)
3. C) (-4, -6) (-7, 8)
4. D) (0, -7) (0, -6)

Answer:  B

Type: BI     Var: 50+

Topic:  5.2 Graphs of Linear Functions

Skill:  Recall

Objective:  (5.2) Find x, y-intercepts

 

8) -4x – 2y = 0

1. A) (-0, -4) (-1, 0)
2. B) (-0, 0) (0, -0)
3. C) (-1, 0) (-4, 0)
4. D) (0, -1) (0, -4)

Answer:  B

Type: BI     Var: 50+

Topic:  5.2 Graphs of Linear Functions

Skill:  Recall

Objective:  (5.2) Find x, y-intercepts

 

6   Solve Apps: Sketch Graph

 

Sketch the indicated line.

 

1) During the month of April 2009, the depth, d, of snow in centimetres at the base of a ski resort in British Columbia could be approximated by d = -1.38t + 43 where t is the number of days after March 30. Sketch the graph.

 

 

1. A)
2. B)

 

1. C)
2. D)

Answer:  C

Type: BI     Var: 1

Topic:  5.2 Graphs of Linear Functions

Skill:  Applied

Objective:  (5.2) Solve Apps: Sketch Graph

 

 

2) Two electric currents I and J (in mA), in part of a circuit in a computer are related by the equation . Sketch J as a function of I. These currents can be negative.

 

 

1. A)
2. B)

 

1. C)
2. D)

Answer:  A

Type: BI     Var: 25

Topic:  5.2 Graphs of Linear Functions

Skill:  Applied

Objective:  (5.2) Solve Apps: Sketch Graph

 

 

5.3   Solving Systems of Two Linear Equations in Two Unknowns Graphically

 

1   Solve System of Equations Graphically (To Tenth)

 

Solve the system by graphing.

 

1) 3x + y= -12

x+ 3y= -20

 

 

1. A) (-2, -3)
2. B) (-2, -6)
3. C) (-6, 6)
4. D) (2, -6)

Answer:  B

Type: BI     Var: 50+

Topic:  5.3 Solving Systems of Two Linear Equations in Two Unknowns Graphically

Skill:  Recall

Objective:  (5.3) Solve System of Equations Graphically (To Tenth)

 

2) 9x – 2y = 30

5x + y = 24

 

 

1. A) (4, 3)
2. B) (3, 1)
3. C) (3, 4)
4. D) (4, -3)

Answer:  A

Type: BI     Var: 1

Topic:  5.3 Solving Systems of Two Linear Equations in Two Unknowns Graphically

Skill:  Recall

Objective:  (5.3) Solve System of Equations Graphically (To Tenth)

 

 

3) x + 7y = -6

-3x – y = 10

 

 

1. A) (-0.4, -3.2)
2. B) (-3.2, -0.4)
3. C) (-3.5, -1.3)
4. D) (-3.8, -1.4)

Answer:  B

Type: BI     Var: 50+

Topic:  5.3 Solving Systems of Two Linear Equations in Two Unknowns Graphically

Skill:  Recall

Objective:  (5.3) Solve System of Equations Graphically (To Tenth)

4) -2x + 2y = 5

6x + 2y = 2

 

 

 

1. A) (-0.4, 2.1)
2. B) (-0.1, -2.1)
3. C) (-0.9, -1.6)
4. D) (2.1, -0.4)

Answer:  A

Type: BI     Var: 50+

Topic:  5.3 Solving Systems of Two Linear Equations in Two Unknowns Graphically

Skill:  Recall

Objective:  (5.3) Solve System of Equations Graphically (To Tenth)

 

5) 2x + 3y = 14

4x + 3y = 16

 

 

1. A) (4, 1)
2. B) (2, 8)
3. C) (1, 4)
4. D) Inconsistent

Answer:  C

Type: BI     Var: 50+

Topic:  5.3 Solving Systems of Two Linear Equations in Two Unknowns Graphically

Skill:  Recall

Objective:  (5.3) Solve System of Equations Graphically (To Tenth)

6) 3x + 2y = 5

-6x – 4y = 5

 

 

1. A) (1.5, -1)
2. B) (-1.5, -1)
3. C) (1, 1)
4. D) Inconsistent

Answer:  D

Type: BI     Var: 1

Topic:  5.3 Solving Systems of Two Linear Equations in Two Unknowns Graphically

Skill:  Recall

Objective:  (5.3) Solve System of Equations Graphically (To Tenth)

 

7) 2x + y = 11

2x + y = 13

 

 

1. A) (8, 3)
2. B) (7, -3)
3. C) Dependent
4. D) Inconsistent

Answer:  D

Type: BI     Var: 50+

Topic:  5.3 Solving Systems of Two Linear Equations in Two Unknowns Graphically

Skill:  Recall

Objective:  (5.3) Solve System of Equations Graphically (To Tenth)

8) 3x + y = 10

12x + 4y = 40

 

 

1. A) (0, 10)
2. B) (5, -5)
3. C) Dependent
4. D) Inconsistent

Answer:  C

Type: BI     Var: 50+

Topic:  5.3 Solving Systems of Two Linear Equations in Two Unknowns Graphically

Skill:  Recall

Objective:  (5.3) Solve System of Equations Graphically (To Tenth)

 

9) 3x – 2y = 4

-6x + 4y = 7

 

 

1. A) (1, 2)
2. B) (2, 1)
3. C) Dependent
4. D) Inconsistent

Answer:  D

Type: BI     Var: 1

Topic:  5.3 Solving Systems of Two Linear Equations in Two Unknowns Graphically

Skill:  Recall

Objective:  (5.3) Solve System of Equations Graphically (To Tenth)

10) x = -y

y + x = 6

 

 

1. A) (1, 1)
2. B) (1, 5)
3. C) Dependent
4. D) Inconsistent

Answer:  D

Type: BI     Var: 1

Topic:  5.3 Solving Systems of Two Linear Equations in Two Unknowns Graphically

Skill:  Recall

Objective:  (5.3) Solve System of Equations Graphically (To Tenth)

 

2   Use Calculator to Solve Graphically (To Tenth)

 

Solve the system to the nearest 0.1 for each variable by using a graphing calculator.

 

1) 3x = -5y – 2

6x + 10y = -4

1. A) x = -1.5; y = -2.5
2. B) x = -0.7; y = -0.4
3. C) Dependent
4. D) Inconsistent

Answer:  C

Type: BI     Var: 50+

Topic:  5.3 Solving Systems of Two Linear Equations in Two Unknowns Graphically

Skill:  Recall

Objective:  (5.3) Use Calculator to Solve Graphically (To Tenth)

 

2) -4x = -4y – 3

12x – 12y = -5

1. A) x = 0.6; y = -0.7
2. B) x = 0.2; y = -0.3
3. C) Dependent
4. D) Inconsistent

Answer:  D

Type: BI     Var: 50+

Topic:  5.3 Solving Systems of Two Linear Equations in Two Unknowns Graphically

Skill:  Recall

Objective:  (5.3) Use Calculator to Solve Graphically (To Tenth)

3) x = -3.0y + 5

-4y = 5.0x – 3

1. A) x = -0.8; y = 2.3
2. B) x = 0.7; y = -2.2
3. C) x = -1.0; y = 2.0
4. D) x = -0.7; y = 2.2

Answer:  C

Type: BI     Var: 50+

Topic:  5.3 Solving Systems of Two Linear Equations in Two Unknowns Graphically

Skill:  Recall

Objective:  (5.3) Use Calculator to Solve Graphically (To Tenth)

 

 

4) 2.9x + 3.5y = 2.2

-4.2x = 4.9y + 3.7

48. A) x = -48.1; y = 41.0
49. B) x = -48.6; y = 40.5
50. C) x = -48.2; y = 41.1
51. D) x = -48.4; y = 40.8

Answer:  D

Type: BI     Var: 50+

Topic:  5.3 Solving Systems of Two Linear Equations in Two Unknowns Graphically

Skill:  Recall

Objective:  (5.3) Use Calculator to Solve Graphically (To Tenth)

 

5) -1.5x – 4.9y = 0.8

-1.5x = 1.7y + 3.9

3. A) x = -3.7; y = 1.0
4. B) x = -2.9; y = 0.7
5. C) x = -4.0; y = 1.1
6. D) x = -3.6; y = 0.7

Answer:  A

Type: BI     Var: 50+

Topic:  5.3 Solving Systems of Two Linear Equations in Two Unknowns Graphically

Skill:  Recall

Objective:  (5.3) Use Calculator to Solve Graphically (To Tenth)

 

6) -5.0v = -4.5t

3.7t + 2.8v = 4.0

1. A) v = 0.4; t = 0.7
2. B) v = 0.7; t = 0.4
3. C) v = 0.8; t = 0.5
4. D) v = 0.6; t = 0.6

Answer:  D

Type: BI     Var: 50+

Topic:  5.3 Solving Systems of Two Linear Equations in Two Unknowns Graphically

Skill:  Recall

Objective:  (5.3) Use Calculator to Solve Graphically (To Tenth)

7) 5x = y – 2

5x = -3.0y + 1

1. A) x = -0.4; y = 0.7
2. B) x = 0.0; y = 0.9
3. C) x = -0.1; y = 1.0
4. D) x = -0.2; y = 0.8

Answer:  D

Type: BI     Var: 50+

Topic:  5.3 Solving Systems of Two Linear Equations in Two Unknowns Graphically

Skill:  Recall

Objective:  (5.3) Use Calculator to Solve Graphically (To Tenth)

 

8) -2.5u – 4.6v = 3.0

-4.5u = 3.9v + 4.0

1. A) u = -0.5; v = -0.1
2. B) u = -0.4; v = -0.2
3. C) u = -0.7; v = -0.5
4. D) u = -0.6; v = -0.3

Answer:  D

Type: BI     Var: 50+

Topic:  5.3 Solving Systems of Two Linear Equations in Two Unknowns Graphically

Skill:  Recall

Objective:  (5.3) Use Calculator to Solve Graphically (To Tenth)

 

9) -3F – 2T = 3

-5F – 5T = 2

2. A) F = -2.4; T = 1.5
3. B) F = -2.2; T = 1.8
4. C) F = -1.9; T = 2.0
5. D) F = -2.0; T = 2.1

Answer:  B

Type: BI     Var: 50+

Topic:  5.3 Solving Systems of Two Linear Equations in Two Unknowns Graphically

Skill:  Recall

Objective:  (5.3) Use Calculator to Solve Graphically (To Tenth)

 

3   Solve Apps: Solve Problem Graphically

 

Solve graphically the problem to the stated accuracy.

 

1) A mother is choosing which baby foods to serve her infant. A jar of meat has  of protein and 34 calories. A jar of vegetables has of protein and 17 calories. How much of each (to the nearest tenth) will she need to serve to get  of protein and 103 calories?

 

1. A) 1.5 jars of meat and 2.0 jars of vegetables
2. B) 2.0 jars of meat and 1.5 jars of vegetables
3. C) There are infinitely many such combinations.
4. D) There is no such combination.

Answer:  D

Type: BI     Var: 50+

Topic:  5.3 Solving Systems of Two Linear Equations in Two Unknowns Graphically

Skill:  Applied

Objective:  (5.3) Solve Apps: Solve Problem Graphically

 

 

5.4   Solving Systems of Two Linear Equations in Two Unknowns Algebraically

 

1   Solve System of Equations by Substitution

 

Solve by the method of elimination by substitution.

 

1) x + y = -1

x – y = 13

1. A) x = 6, y = -7
2. B) x = -6, y = -6
3. C) x = 5, y = -6
4. D) Inconsistent

Answer:  A

Type: BI     Var: 50+

Topic:  5.4 Solving Systems of Two Linear Equations in Two Unknowns Algebraically

Skill:  Recall

Objective:  (5.4) Solve System of Equations by Substitution

2) x – 3y = -21

7x – 3y = -57

1. A) x = -5, y = 4
2. B) x = -6, y = 5
3. C) x = 6, y = 4
4. D) Inconsistent

Answer:  B

Type: BI     Var: 50+

Topic:  5.4 Solving Systems of Two Linear Equations in Two Unknowns Algebraically

Skill:  Recall

Objective:  (5.4) Solve System of Equations by Substitution

 

3) x – 5y = -34

2x – 5y = -28

1. A) x = 6, y = 8
2. B) x = 7, y = 6
3. C) x = 7, y = 7
4. D) Inconsistent

Answer:  A

Type: BI     Var: 50+

Topic:  5.4 Solving Systems of Two Linear Equations in Two Unknowns Algebraically

Skill:  Recall

Objective:  (5.4) Solve System of Equations by Substitution

 

 

4) x + 2y = 0

x – 2y = 32

1. A) x = 16, y = -8
2. B) x = 2, y = -1
3. C) x = 16, y = 8
4. D) x = -8, y = 16

Answer:  A

Type: BI     Var: 50+

Topic:  5.4 Solving Systems of Two Linear Equations in Two Unknowns Algebraically

Skill:  Recall

Objective:  (5.4) Solve System of Equations by Substitution

 

5) 7x – 4y = 28

4x + 2y = 46

1. A) x = -8, y = 7
2. B) x = -4, y = -8
3. C) x = 8, y = 7
4. D) Inconsistent

Answer:  C

Type: BI     Var: 50+

Topic:  5.4 Solving Systems of Two Linear Equations in Two Unknowns Algebraically

Skill:  Recall

Objective:  (5.4) Solve System of Equations by Substitution

6) 6x + 9y = 8

6x + 9y = 15

1. A) x = 6, y = 9
2. B) x = 1, y = 1
3. C) Dependent
4. D) Inconsistent

Answer:  D

Type: BI     Var: 50+

Topic:  5.4 Solving Systems of Two Linear Equations in Two Unknowns Algebraically

Skill:  Recall

Objective:  (5.4) Solve System of Equations by Substitution

 

7) 5x + 5y = 6

3x + 3y = 6

1. A) x = 1, y = 1
2. B) x = 2, y = 3
3. C) Dependent
4. D) Inconsistent

Answer:  D

Type: BI     Var: 50+

Topic:  5.4 Solving Systems of Two Linear Equations in Two Unknowns Algebraically

Skill:  Recall

Objective:  (5.4) Solve System of Equations by Substitution

 

8) 5x + 3y = -9

2x + 2y = -2

1. A) x = -6, y = 4
2. B) x = 3, y = 2
3. C) x = -3, y = 2
4. D) Inconsistent

Answer:  C

Type: BI     Var: 50+

Topic:  5.4 Solving Systems of Two Linear Equations in Two Unknowns Algebraically

Skill:  Recall

Objective:  (5.4) Solve System of Equations by Substitution

 

9) 0.1x + 0.5y = -0.7

x – 0.8y = -1.2

1. A) x = -0.2, y = -0.1
2. B) x = -2, y = -1
3. C) x = -1, y = -2
4. D) Inconsistent

Answer:  B

Type: BI     Var: 50+

Topic:  5.4 Solving Systems of Two Linear Equations in Two Unknowns Algebraically

Skill:  Recall

Objective:  (5.4) Solve System of Equations by Substitution

10) 0.04x + 0.08y = 0.28

-0.04x + y = 2.96

1. A) x = 1, y = 3
2. B) x = 3, y = 1
3. C) x = 0.1, y = 0.3
4. D) Inconsistent

Answer:  A

Type: BI     Var: 50+

Topic:  5.4 Solving Systems of Two Linear Equations in Two Unknowns Algebraically

Skill:  Recall

Objective:  (5.4) Solve System of Equations by Substitution

 

 

2   Solve System of Equations by Addition or Subtraction

 

Solve by the method of elimination by addition or subtraction.

 

1) x – 3y = 26

4x – 4y = 48

1. A) x = -5, y = -6
2. B) x = 5, y = -7
3. C) x = 4, y = -6
4. D) Inconsistent

Answer:  B

Type: BI     Var: 50+

Topic:  5.4 Solving Systems of Two Linear Equations in Two Unknowns Algebraically

Skill:  Recall

Objective:  (5.4) Solve System of Equations by Addition or Subtraction

 

2) x + 4y =  8

-3x + 5y = 10

1. A) x = 0, y = 2
2. B) x = -2, y = 0
3. C) x = 1, y = 1
4. D) Inconsistent

Answer:  A

Type: BI     Var: 50+

Topic:  5.4 Solving Systems of Two Linear Equations in Two Unknowns Algebraically

Skill:  Recall

Objective:  (5.4) Solve System of Equations by Addition or Subtraction

 

3) x – 3y =  7

7x – 2y = 49

1. A) x = 8, y = -1
2. B) x = 7, y = 0
3. C) x = 8, y = 7
4. D) Inconsistent

Answer:  B

Type: BI     Var: 50+

Topic:  5.4 Solving Systems of Two Linear Equations in Two Unknowns Algebraically

Skill:  Recall

Objective:  (5.4) Solve System of Equations by Addition or Subtraction

 

4) -5x + 9y = -71

-2x + 2y = -22

1. A) x = 6, y = -3
2. B) x = 7, y = -4
3. C) x = 7, y = -3
4. D) Inconsistent

Answer:  B

Type: BI     Var: 50+

Topic:  5.4 Solving Systems of Two Linear Equations in Two Unknowns Algebraically

Skill:  Recall

Objective:  (5.4) Solve System of Equations by Addition or Subtraction

 

5)  7x – 4y = 16

2x – 2y =  8

1. A) x = -1, y = -3
2. B) x = 0, y = -3
3. C) x = 0, y = -4
4. D) Inconsistent

Answer:  C

Type: BI     Var: 50+

Topic:  5.4 Solving Systems of Two Linear Equations in Two Unknowns Algebraically

Skill:  Recall

Objective:  (5.4) Solve System of Equations by Addition or Subtraction

 

6)  5x + 8y = -5

3x – 5y = -3

1. A) x = -1, y = 0
2. B) x = -1, y = 1
3. C) x = -2, y = 1
4. D) Inconsistent

Answer:  A

Type: BI     Var: 50+

Topic:  5.4 Solving Systems of Two Linear Equations in Two Unknowns Algebraically

Skill:  Recall

Objective:  (5.4) Solve System of Equations by Addition or Subtraction

 

7)  9x + 62 =  7y

-6x – 2y =  8

1. A) x = -4, y = 6
2. B) x = -3, y = 6
3. C) x = -3, y = 5
4. D) Inconsistent

Answer:  C

Type: BI     Var: 50+

Topic:  5.4 Solving Systems of Two Linear Equations in Two Unknowns Algebraically

Skill:  Recall

Objective:  (5.4) Solve System of Equations by Addition or Subtraction

8) -6x – 5y = -12

-12x = -14 + 10y

1. A) x = -6, y = -4
2. B) x = -3, y = 6
3. C) x = -3, y = -4
4. D) Inconsistent

Answer:  D

Type: BI     Var: 50+

Topic:  5.4 Solving Systems of Two Linear Equations in Two Unknowns Algebraically

Skill:  Recall

Objective:  (5.4) Solve System of Equations by Addition or Subtraction

 

9)  –  = -18

+  = -9

1. A) x = 12, y = 0
2. B) x = 0, y = -12
3. C) x = 0, y = 12
4. D) x = -12, y = 0

Answer:  D

Type: BI     Var: 1

Topic:  5.4 Solving Systems of Two Linear Equations in Two Unknowns Algebraically

Skill:  Recall

Objective:  (5.4) Solve System of Equations by Addition or Subtraction

 

10) = 5

9x = 10 + 9y

1. A) x = , y =
2. B) x = , y =
3. C) x = , y =
4. D) x = , y =

Answer:  D

Type: BI     Var: 6

Topic:  5.4 Solving Systems of Two Linear Equations in Two Unknowns Algebraically

Skill:  Recall

Objective:  (5.4) Solve System of Equations by Addition or Subtraction

 

3   Solve Apps: Solve System of Equations Algebraically

 

Solve the problem.

 

1) A sprinkler system is used to water two areas. If the total water flow is 560 L/h and the flow through one sprinkler is 65 times greater than the other, what is the flow in each at the nearest hundredth?

551. A) 551.52 L/h, 8.62 L/h
552. B) 8.48 L/h, 8.36 L/h
553. C) 551.52 L/h, 8.48 L/h
554. D) 551.52 L/h, 8.36 L/h

Answer:  C

Type: BI     Var: 50+

Topic:  5.4 Solving Systems of Two Linear Equations in Two Unknowns Algebraically

Skill:  Applied

Objective:  (5.4) Solve Apps: Solve System of Equations Algebraically

 

2) There were 35,000 people at a ball game in Los Angeles. The day’s receipts were $238,000. How many people paid $14 for reserved seats and how many paid $5 for general admission?

1. A) 15,750 paid $14 and 19,250 paid $5
2. B) 19,250 paid $14 and 15,750 paid $5
3. C) 28,000 paid $14 and 7000 paid $5
4. D) 7000 paid $14 and 28,000 paid $5

Answer:  D

Type: BI     Var: 50+

Topic:  5.4 Solving Systems of Two Linear Equations in Two Unknowns Algebraically

Skill:  Applied

Objective:  (5.4) Solve Apps: Solve System of Equations Algebraically

 

 

5.5   Solving Systems of Two Linear Equations in Two Unknowns by Determinants

 

1   Evaluate 2×2 Determinant

 

Evaluate the determinant.

 

1)

1. A) -37
2. B) -7
3. C) 49
4. D) 7

Answer:  D

Type: BI     Var: 50+

Topic:  5.5 Solving Systems of Two Linear Equations in Two Unknowns by Determinants

Skill:  Recall

Objective:  (5.5) Evaluate 2×2 Determinant

2)

1. A) -46
2. B) 26
3. C) -26
4. D) 37

Answer:  B

Type: BI     Var: 50+

Topic:  5.5 Solving Systems of Two Linear Equations in Two Unknowns by Determinants

Skill:  Recall

Objective:  (5.5) Evaluate 2×2 Determinant

 

3)

1. A) 0
2. B) 5
3. C) 3
4. D) -3

Answer:  D

Type: BI     Var: 50+

Topic:  5.5 Solving Systems of Two Linear Equations in Two Unknowns by Determinants

Skill:  Recall

Objective:  (5.5) Evaluate 2×2 Determinant

 

 

2   Solve System of Equations by Determinants

 

Solve the system of equations by determinants.

 

1) 2x + 2y = -4

2x + y = -6

1. A) x = -4, y = 2
2. B) x = -2, y = -4
3. C) x = 2, y = -4
4. D) x = 4, y = -2

Answer:  A

Type: BI     Var: 50+

Topic:  5.5 Solving Systems of Two Linear Equations in Two Unknowns by Determinants

Skill:  Recall

Objective:  (5.5) Solve System of Equations by Determinants

 

2)  4x + 3y = 18

3x + 5y = 19

1. A) x = -3, y = -2
2. B) x = 2, y = 3
3. C) x = -2, y = 3
4. D) x = 3, y = 2

Answer:  D

Type: BI     Var: 50+

Topic:  5.5 Solving Systems of Two Linear Equations in Two Unknowns by Determinants

Skill:  Recall

Objective:  (5.5) Solve System of Equations by Determinants

3) 3x + 3y = 45

2x – 2y = -6

1. A) x = 9, y = 6
2. B) x = -6, y = -9
3. C) x = -9, y = 6
4. D) x = 6, y = 9

Answer:  D

Type: BI     Var: 50+

Topic:  5.5 Solving Systems of Two Linear Equations in Two Unknowns by Determinants

Skill:  Recall

Objective:  (5.5) Solve System of Equations by Determinants

 

 

4) x + 4y = 17

5x + y = 8

1. A) x = – , y = –
2. B) x = , y = –
3. C) x = – , y =
4. D) x = , y =

Answer:  D

Type: BI     Var: 50+

Topic:  5.5 Solving Systems of Two Linear Equations in Two Unknowns by Determinants

Skill:  Recall

Objective:  (5.5) Solve System of Equations by Determinants

 

5)   6x –  9y = -2

18x – 27y =  -7

1. A) x = 3, y = 3
2. B) x = -2, y = -7
3. C) Dependent
4. D) Inconsistent

Answer:  D

Type: BI     Var: 50+

Topic:  5.5 Solving Systems of Two Linear Equations in Two Unknowns by Determinants

Skill:  Recall

Objective:  (5.5) Solve System of Equations by Determinants

 

6) 0.4x + 0.9y = -1.1

x – 0.4y = -5.4

1. A) x = -0.5, y = 0.1
2. B) x = 1, y = -5
3. C) x = -5, y = 1
4. D) Inconsistent

Answer:  C

Type: BI     Var: 50+

Topic:  5.5 Solving Systems of Two Linear Equations in Two Unknowns by Determinants

Skill:  Recall

Objective:  (5.5) Solve System of Equations by Determinants

 

7) 2.5x – 0.9y = 4.1

-7.5x + 2.7y = -12.3

4. A) x = 0, y = -4.6
5. B) x = 1.6, y = 0
6. C) Dependent
7. D) Inconsistent

Answer:  C

Type: BI     Var: 1

Topic:  5.5 Solving Systems of Two Linear Equations in Two Unknowns by Determinants

Skill:  Recall

Objective:  (5.5) Solve System of Equations by Determinants

 

8) A system of equations is described as inconsistent if both solutions yield an indeterminant division.

Answer:  FALSE

Type: TF     Var: 1

Topic:  5.5 Solving Systems of Two Linear Equations in Two Unknowns by Determinants

Skill:  Recall

Objective:  (5.5) Solve System of Equations by Determinants

 

9) A system of equations is described as inconsistent if both solutions yield a division by zero error (division by zero with non-zero in numerator).

Answer:  TRUE

Type: TF     Var: 1

Topic:  5.5 Solving Systems of Two Linear Equations in Two Unknowns by Determinants

Skill:  Recall

Objective:  (5.5) Solve System of Equations by Determinants

 

 

3   Solve Apps: Solve System of Equations by Determinants

 

Solve the problem. Round approximations to an appropriate number of significant digits.

 

1) A mechanic has some 30% antifreeze solution and some 50% solution. How many liters of each should be used to get 25 liters of a 42% solution?

10. A) 10.5 liters at 30%

14.5 liters at 50%

1. B) 10 liters at 30%

15 liters at 50%

1. C) 15 liters at 30%

10 liters at 50%

1. D) 11 liters at 30%

14 liters at 50%

Answer:  B

Type: BI     Var: 14

Topic:  5.5 Solving Systems of Two Linear Equations in Two Unknowns by Determinants

Skill:  Applied

Objective:  (5.5) Solve Apps: Solve System of Equations by Determinants

2) At a book sale, Ruth bought 5 hardbacks and 2 paperbacks for $46.00. She returned later and bought 1 more hardback and 3 more paperbacks for $17.00.  Find the cost of a hardback and the cost of a paperback at the book sale.

10. A) $10.00 for hardback

$3.00 for paperback

3. B) $3.00 for hardback

$8.00 for paperback

8. C) $8.00 for hardback

$3.00 for paperback

7. D) $7.50 for hardback

$3.50 for paperback

Answer:  C

Type: BI     Var: 24

Topic:  5.5 Solving Systems of Two Linear Equations in Two Unknowns by Determinants

Skill:  Applied

Objective:  (5.5) Solve Apps: Solve System of Equations by Determinants

 

 

5.6   Solving Systems of Three Linear Equations in Three Unknowns Algebraically

 

1   Solve System of Three Equations

 

Solve the system of equations.

 

1) x + y + z = -2

x – y + 2z = -5

3x + y + z = -12

1. A) x = 1, y = 2, z = -5
2. B) x = -5, y = 2, z = 1
3. C) x = 1, y = -5, z = 2
4. D) Inconsistent

Answer:  B

Type: BI     Var: 50+

Topic:  5.6 Solving Systems of Three Linear Equations in Three Unknowns Algebraically

Skill:  Recall

Objective:  (5.6) Solve System of Three Equations

 

2) x – y + z = 8

x + y + z = 6

x + y – z = 2

1. A) x = 2, y = 5, z = -1
2. B) x = 5, y = 2, z = -1
3. C) x = 5, y = -1, z = 2
4. D) Inconsistent

Answer:  C

Type: BI     Var: 50+

Topic:  5.6 Solving Systems of Three Linear Equations in Three Unknowns Algebraically

Skill:  Recall

Objective:  (5.6) Solve System of Three Equations

3) x + 5y + 5z = 10

2y + 2z =  6

z =  4

1. A) x = -5, y = 4, z = -1
2. B) x = 4, y = -1, z = -5
3. C) x = -5, y = -1, z = 4
4. D) Inconsistent

Answer:  C

Type: BI     Var: 50+

Topic:  5.6 Solving Systems of Three Linear Equations in Three Unknowns Algebraically

Skill:  Recall

Objective:  (5.6) Solve System of Three Equations

 

 

4) 4x + 2y + z = 24

2x – 3y – z =  2

5x + y + 2z = 21

1. A) x = 5, y = 4, z = -4
2. B) x = -4, y = 4, z = 5
3. C) x = 5, y = -4, z = 4
4. D) Inconsistent

Answer:  A

Type: BI     Var: 50+

Topic:  5.6 Solving Systems of Three Linear Equations in Three Unknowns Algebraically

Skill:  Recall

Objective:  (5.6) Solve System of Three Equations

 

5) x – y + 5z = -17

5x + z = -3

x + 5y + z = 7

1. A) x = 2, y = 0, z = -3
2. B) x = 0, y = 2, z = -3
3. C) x = -3, y = 2, z = 0
4. D) Inconsistent

Answer:  B

Type: BI     Var: 50+

Topic:  5.6 Solving Systems of Three Linear Equations in Three Unknowns Algebraically

Skill:  Recall

Objective:  (5.6) Solve System of Three Equations

 

6) 3x – y = 20

2y + z = 22

x + 4z = 41

1. A) x = 9, y = 7, z = 8
2. B) x = 18, y = 14, z = 16
3. C) x = -9, y = -7, z = -8
4. D) Inconsistent

Answer:  A

Type: BI     Var: 50+

Topic:  5.6 Solving Systems of Three Linear Equations in Three Unknowns Algebraically

Skill:  Recall

Objective:  (5.6) Solve System of Three Equations

 

7) x – y + 3z = 5

3x + z = 0

x + 4y + z = -20

1. A) x = 0, y = 0, z = -5
2. B) x = 0, y = -5, z = 0
3. C) x = 0, y = -5, z = 5
4. D) Inconsistent

Answer:  B

Type: BI     Var: 50+

Topic:  5.6 Solving Systems of Three Linear Equations in Three Unknowns Algebraically

Skill:  Recall

Objective:  (5.6) Solve System of Three Equations

 

8) 3x – 4y = -3

6x + 2z = –

2y – 4z = 4

1. A) x = 3, y = 3, z =
2. B) x = – , y = , z = –
3. C) x = – , y = , z =
4. D) Inconsistent

Answer:  B

Type: BI     Var: 1

Topic:  5.6 Solving Systems of Three Linear Equations in Three Unknowns Algebraically

Skill:  Recall

Objective:  (5.6) Solve System of Three Equations

 

 

2   Solve Apps: Solve System of Three Equations

 

Solve the problem.

 

1) In triangle ABC, the measure of angle B is 5° more than three times the measure of angle A. The measure of angle C is 15° more than the measure of angle A. Find the angle measures.

1. A) A = 32°, B = 47°, C = 101°
2. B) A = 32°, B = 101°, C = 47°
3. C) A = 47°, B = 101°, C = 32°
4. D) No solution

Answer:  B

Type: MC     Var: 1

Topic:  5.6 Solving Systems of Three Linear Equations in Three Unknowns Algebraically

Skill:  Recall

Objective:  (5.6) Solve Apps: Solve System of Three Equations

2) The sum of three numbers is 6. The first, minus the second, plus 2 times the third, is -7. The third, plus 2 times the first, plus the second, is 10. What are the numbers?

1. A) 4, 5, -3
2. B) -4, -5, 3
3. C) 4, 4, 5
4. D) No solution

Answer:  A

Type: BI     Var: 50+

Topic:  5.6 Solving Systems of Three Linear Equations in Three Unknowns Algebraically

Skill:  Recall

Objective:  (5.6) Solve Apps: Solve System of Three Equations

 

3) A $128,000 trust is to be invested in bonds paying 6%, CDs paying 5%, and mortgages paying 7%. The sum of the bond and CD investment must equal the mortgage investment. To earn an $7900 annual income from the investments, how much should the bank invest in bonds?

1. A) $22,000
2. B) $64,000
3. C) $42,000
4. D) $20,000

Answer:  A

Type: BI     Var: 50+

Topic:  5.6 Solving Systems of Three Linear Equations in Three Unknowns Algebraically

Skill:  Recall

Objective:  (5.6) Solve Apps: Solve System of Three Equations

 

 

4) The sum of a student’s three scores is 217. If the first is 16 points more than the second, and the sum of the first two is 28 more than twice the third, what was the first score?

1. A) 47
2. B) 85
3. C) 69
4. D) 63

Answer:  B

Type: BI     Var: 50+

Topic:  5.6 Solving Systems of Three Linear Equations in Three Unknowns Algebraically

Skill:  Recall

Objective:  (5.6) Solve Apps: Solve System of Three Equations

 

5) Michael’s bank contains only nickels, dimes, and quarters. There are 50 coins in all, valued at $4.15. The number of nickels is 10 short of being three times the sum of the number of dimes and quarters together. How many dimes are in the bank?

1. A) 14
2. B) 6
3. C) 9
4. D) 35

Answer:  C

Type: BI     Var: 50+

Topic:  5.6 Solving Systems of Three Linear Equations in Three Unknowns Algebraically

Skill:  Recall

Objective:  (5.6) Solve Apps: Solve System of Three Equations

6) Some people must eat a low-sodium diet with no more than 2,000 mg of sodium per day. By eating 1 cracker, 1 pretzel, and 1 cookie, a person would ingest 149 mg of sodium. If a person ate 8 pretzels and 8 cookies, he or she would ingest 936 mg of sodium. By eating 6 crackers and 7 pretzels, the person would take in 535 mg of sodium. Find the amount of sodium in each.

 

Which of the following is true?

1. A) A cracker has 30 mg of sodium.
2. B) A cookie has 71 mg of sodium.
3. C) A pretzel has 49 mg of sodium.
4. D) None of these

Answer:  C

Type: MC     Var: 1

Topic:  5.6 Solving Systems of Three Linear Equations in Three Unknowns Algebraically

Skill:  Recall

Objective:  (5.6) Solve Apps: Solve System of Three Equations

 

 

3   Solve System of Three Equations if Inconsistent or Dependent

 

Solve the system. If there is an unlimited number of solutions, find one of them.

 

1) x + y + z = -1

x – y + 4z = -5

2x + 2y + 2z = 0

1. A) x = -4, y = 2, z = 1
2. B) x = -4, y = 1, z = 2
3. C) x = 1, y = 2, z = -4
4. D) Inconsistent

Answer:  D

Type: BI     Var: 50+

Topic:  5.6 Solving Systems of Three Linear Equations in Three Unknowns Algebraically

Skill:  Applied

Objective:  (5.6) Solve System of Three Equations if Inconsistent or Dependent

 

2) x – y + 3z = 17

-3x + 3y –  9z = 4

x + 3y + z = 19

1. A) x = 4, x = 0, y = 5
2. B) x = 4, y = 5, z = 0
3. C) x = 0, y = 5, z = 4
4. D) Inconsistent

Answer:  D

Type: BI     Var: 50+

Topic:  5.6 Solving Systems of Three Linear Equations in Three Unknowns Algebraically

Skill:  Applied

Objective:  (5.6) Solve System of Three Equations if Inconsistent or Dependent

3) 2x +  6y + 10z = 155

x +  3y +  5z = -31

x + y + z = -5

1. A) x = -5, y = 1, z = -2
2. B) x = 1, y = -2, z = -5
3. C) Unlimited: x = -5, y = -2, z = 1
4. D) Inconsistent

Answer:  D

Type: BI     Var: 50+

Topic:  5.6 Solving Systems of Three Linear Equations in Three Unknowns Algebraically

Skill:  Applied

Objective:  (5.6) Solve System of Three Equations if Inconsistent or Dependent

 

 

4) x + y + z = 9

2x – 3y + 4z = 7

x – 4y + 3z = -2

1. A) x = 1, y = 1, z = 1
2. B) x = 9, y = 7, z = 2
3. C) Unlimited: x = , y = , z = 0
4. D) Inconsistent

Answer:  C

Type: BI     Var: 1

Topic:  5.6 Solving Systems of Three Linear Equations in Three Unknowns Algebraically

Skill:  Applied

Objective:  (5.6) Solve System of Three Equations if Inconsistent or Dependent

 

5) x + y – 2z = 8

3x + z = -6

2x – y + 3z = -14

1. A) x = 1, y = 1, z = -2
2. B) x = -1, y = -2, z = 2
3. C) Unlimited: x = -2, y = 10, z = 0
4. D) Inconsistent

Answer:  C

Type: BI     Var: 1

Topic:  5.6 Solving Systems of Three Linear Equations in Three Unknowns Algebraically

Skill:  Applied

Objective:  (5.6) Solve System of Three Equations if Inconsistent or Dependent

6) 3x + 2y + z = 4

2x – 3y – z = 5

5x + 12y + 5z = 2

1. A) x = -4, y = 5, z = -2
2. B) x = 4, y = 5, z = 2
3. C) Unlimited: x = , y = , z = 0
4. D) Inconsistent

Answer:  C

Type: BI     Var: 1

Topic:  5.6 Solving Systems of Three Linear Equations in Three Unknowns Algebraically

Skill:  Applied

Objective:  (5.6) Solve System of Three Equations if Inconsistent or Dependent

 

 

5.7   Solving Systems of Three Linear Equations in Three Unknowns by Determinants

 

1   Evaluate Third Order Determinant

 

Evaluate the determinant.

 

1)

1. A) 1515
2. B) -31
3. C) 31
4. D) -451

Answer:  B

Type: BI     Var: 50+

Topic:  5.7 Solving Systems of Three Linear Equations in Three Unknowns by Determinants

Skill:  Recall

Objective:  (5.7) Evaluate Third Order Determinant

 

2)

1. A) -93
2. B) -213
3. C) 93
4. D) 127

Answer:  A

Type: BI     Var: 50+

Topic:  5.7 Solving Systems of Three Linear Equations in Three Unknowns by Determinants

Skill:  Recall

Objective:  (5.7) Evaluate Third Order Determinant

3)

1. A) 86
2. B) 16
3. C) -48
4. D) -16

Answer:  D

Type: BI     Var: 50+

Topic:  5.7 Solving Systems of Three Linear Equations in Three Unknowns by Determinants

Skill:  Recall

Objective:  (5.7) Evaluate Third Order Determinant

 

4)

1. A) 368
2. B) -148
3. C) -100
4. D) 100

Answer:  C

Type: BI     Var: 50+

Topic:  5.7 Solving Systems of Three Linear Equations in Three Unknowns by Determinants

Skill:  Recall

Objective:  (5.7) Evaluate Third Order Determinant

 

5)

1. A) -26
2. B) -54
3. C) 14
4. D) -14

Answer:  D

Type: BI     Var: 50+

Topic:  5.7 Solving Systems of Three Linear Equations in Three Unknowns by Determinants

Skill:  Recall

Objective:  (5.7) Evaluate Third Order Determinant

6)

1. A) -10
2. B) 35
3. C) -35
4. D) -80

Answer:  C

Type: BI     Var: 50+

Topic:  5.7 Solving Systems of Three Linear Equations in Three Unknowns by Determinants

Skill:  Recall

Objective:  (5.7) Evaluate Third Order Determinant

 

 

7)

1. A) 195
2. B) -255
3. C) -225
4. D) 225

Answer:  D

Type: BI     Var: 50+

Topic:  5.7 Solving Systems of Three Linear Equations in Three Unknowns by Determinants

Skill:  Recall

Objective:  (5.7) Evaluate Third Order Determinant

 

8)

469. A) 469.932
470. B) 442.188
471. C) 512.688
472. D) 426.228

Answer:  C

Type: BI     Var: 50+

Topic:  5.7 Solving Systems of Three Linear Equations in Three Unknowns by Determinants

Skill:  Recall

Objective:  (5.7) Evaluate Third Order Determinant

 

2   Solve System by Determinants

 

Solve the system of equations by use of determinants.

 

1)  4x + 7y – z = 67

x + 7y + 2z = 82

9x + y + z = 44

1. A) x = 3, y = 9, z = 8
2. B) x = 4, y = 7, z = 8
3. C) x = 9, y = 8, z = 9
4. D) x = 3, y = -9, z = -8

Answer:  A

Type: BI     Var: 50+

Topic:  5.7 Solving Systems of Three Linear Equations in Three Unknowns by Determinants

Skill:  Applied

Objective:  (5.7) Solve System by Determinants

 

2) -2x – 7y + 6z = -57

5x + 8y – 5z = 97

-4x – 3y – 6z = -87

1. A) x = 9, y = 9, z = 4
2. B) x = 9, y = -9, z = -4
3. C) x = 9, y= 4, z = 9
4. D) x = 10, y = 7, z = 4

Answer:  A

Type: BI     Var: 50+

Topic:  5.7 Solving Systems of Three Linear Equations in Three Unknowns by Determinants

Skill:  Applied

Objective:  (5.7) Solve System by Determinants

 

3) -2x – 8z = -80

2x + 4y + 8z = 104

-8x – 4y = -56

1. A) x = 6, y = 9, z = 6
2. B) x = 5, y = 4, z = 9
3. C) x = 4, y = -6, z = -9
4. D) x = 4, y = 6, z = 9

Answer:  D

Type: BI     Var: 50+

Topic:  5.7 Solving Systems of Three Linear Equations in Three Unknowns by Determinants

Skill:  Applied

Objective:  (5.7) Solve System by Determinants

 

4) y + z = 4

3x- z = 5

2x + y + 3z = 2

1. A) x = 2, y = 12, z = – 4
2. B) x = , y = 3, z = – 1
3. C) x = – 1, y = – 6, z = 2
4. D) x = 1, y = 6, z = – 2

Answer:  D

Type: BI     Var: 50+

Topic:  5.7 Solving Systems of Three Linear Equations in Three Unknowns by Determinants

Skill:  Applied

Objective:  (5.7) Solve System by Determinants

 

3   Solve Apps: Solve System of Equations by Determinants

 

Solve the problem.

 

1) The mode equations for a circuit follow:

 

 

What are the node voltages , , and ?

1. A) = 100 V, = 120 V,  = 100 V
2. B) = 100 V, = -120 V,  = -1500 V
3. C) = 100 V, = -120 V,  = 100 V
4. D) = 100 V, = 120 V,  = 1500 V

Answer:  A

Type: BI     Var: 50+

Topic:  5.7 Solving Systems of Three Linear Equations in Three Unknowns by Determinants

Skill:  Applied

Objective:  (5.7) Solve Apps: Solve System of Equations by Determinants

 

2) The sum of a student’s three scores is 218. If the first is 12 points more than the second, and the sum of the first two is 26 more than twice the third, what was the first score?

1. A) 71
2. B) 64
3. C) 52
4. D) 83

Answer:  D

Type: BI     Var: 50+

Topic:  5.7 Solving Systems of Three Linear Equations in Three Unknowns by Determinants

Skill:  Applied

Objective:  (5.7) Solve Apps: Solve System of Equations by Determinants

3) A $78,000 trust is to be invested in bonds paying 7%, CDs paying 6%, and mortgages paying 10%. The bond and CD investment must equal the mortgage investment. To earn an annual income of $6340 from the investments, how much should the bank invest in bonds?

1. A) $10,000
2. B) $39,000
3. C) $29,000
4. D) $8,000

Answer:  A

Type: BI     Var: 50+

Topic:  5.7 Solving Systems of Three Linear Equations in Three Unknowns by Determinants

Skill:  Applied

Objective:  (5.7) Solve Apps: Solve System of Equations by Determinants

 

4) Michael’s bank contains only nickels, dimes, and quarters. There are 52 coins in all, valued at $4.55. The number of nickels is 8 short of being three times the sum of the number of dimes and quarters together. How many dimes are in the bank?

1. A) 37
2. B) 8
3. C) 7
4. D) 12

Answer:  C

Type: BI     Var: 50+

Topic:  5.7 Solving Systems of Three Linear Equations in Three Unknowns by Determinants

Skill:  Applied

Objective:  (5.7) Solve Apps: Solve System of Equations by Determinants

 

5) Three unknown forces are exerted at the pin joint shown in a static structure. It is known that the sum of the magnitudes of the three forces is 85 N. Analysing the force components in the horizontal and vertical directions yields two more equations:

 

-0.566  – 0.789  + 0.727  = 0

0.862  – 0.332  – 0.275  = 0

 

Find the magnitude of .

21. A) 21.7 N
22. B) 41.0 N
23. C) 22.3 N
24. D) 21.6 N

Answer:  A

Type: BI     Var: 1

Topic:  5.7 Solving Systems of Three Linear Equations in Three Unknowns by Determinants

Skill:  Applied

Objective:  (5.7) Solve Apps: Solve System of Equations by Determinants

 

6) Three unknown forces are exerted at the pin joint shown in a static structure. It is known that the sum of the magnitudes of forces  and  is 88 kN. Analysing the force components in the horizontal and vertical directions yields two more equations:

 

0.86  – 0.92  + 0.44  = 0

0.71  – 0.33  – 0.25  = 0

 

Find the magnitude of .

1. A) 37 kN
2. B) 88 kN
3. C) 52 kN
4. D) 36 kN

Answer:  C

Type: BI     Var: 1

Topic:  5.7 Solving Systems of Three Linear Equations in Three Unknowns by Determinants

Skill:  Applied

Objective:  (5.7) Solve Apps: Solve System of Equations by Determinants