Systems Of Linear Equations And Inequalities Exam Prep Ch.6

College Algebra, 5e (Young)

Chapter 6 Systems of Linear Equations and Inequalities

6.1 Systems of Linear Equations in Two Variables

1) Solve the system of linear equations by substitution.

5x + 2y = -19

8x - 4y = -52

A) (5, -3)

B) (-5, 3)

C) (-5, -3)

D) (5, 3)

Diff: 2 Var: 1

Chapter/Section: Ch 06, Sec 01

Learning Objective: Solve systems of linear equations in two variables using the substitution method.

2) Solve the system of linear equations by substitution.

2x - 8y = 12

6x - 7y = -15

A) (6, -3)

B) (-3, -6)

C) (-6, -3)

D) (6, 3)

Diff: 2 Var: 1

Chapter/Section: Ch 06, Sec 01

Learning Objective: Solve systems of linear equations in two variables using the substitution method.

3) Solve the system of linear equations by substitution.

2z - 7w = 18

2z - 7w = 5

A) (2, 7)

B) (18, 5)

C) infinite number of solutions

D) no solution

Diff: 2 Var: 1

Chapter/Section: Ch 06, Sec 01

Learning Objective: Solve systems of linear equations in two variables using the substitution method.

4) Solve the system of linear equations by substitution.

-9p - 3q = -45

-18p - 6q = -90

A) (3, 6)

B) (-1, 1)

C) infinite number of solutions

D) no solution

Diff: 2 Var: 1

Chapter/Section: Ch 06, Sec 01

Learning Objective: Solve systems of linear equations in two variables using the substitution method.

5) Solve the system of linear equations by elimination.

5d + 7f = 16

-5d - 3f = -24

A) (6, -2)

B) (-2, 6)

C) (-6, -2)

D) (-2, -6)

Diff: 1 Var: 1

Chapter/Section: Ch 06, Sec 01

Learning Objective: Solve systems of linear equations in two variables using the elimination method.

6) Solve the system of linear equations by elimination.

3x - 14y = 52

6x - 28y = -104

A) (-8, 2)

B) (8, -2)

C) infinite number of solutions

D) no solution

Diff: 2 Var: 1

Chapter/Section: Ch 06, Sec 01

Learning Objective: Solve systems of linear equations in two variables using the elimination method.

7) Solve the system of linear equations by elimination.

-9x - 2y = 72

-18x + 6y = 54

A) (6, 9)

B) (9, 6)

C) (-9, -6)

D) (-6, -9)

Diff: 2 Var: 1

Chapter/Section: Ch 06, Sec 01

Learning Objective: Solve systems of linear equations in two variables using the elimination method.

8) Solve the system of linear equations by elimination.

9t + 10q = -112

27t + 13q = -268

A) (8, -4)

B) (-8, -4)

C) (-4, -8)

D) (-4, 8)

E) None of the above.

Diff: 2 Var: 1

Chapter/Section: Ch 06, Sec 01

Learning Objective: Solve systems of linear equations in two variables using the elimination method.

9) Solve the system of linear equations by graphing the following equations.

2x + 4y = -2

9x + 8y = 21

A) (5, -3)

B) (-3, 5)

C) (-5, -3)

D) (5, 3)

Diff: 2 Var: 1

Chapter/Section: Ch 06, Sec 01

Learning Objective: Solve systems of linear equations in two variables using the elimination method.

10) Solve the system of linear equations by graphing the following equations.

-10x + 5y = 110

-7x + 4y = 81

A) (8, -7)

B) (-7, 8)

C) (7, 8)

D) (8, 7)

Diff: 2 Var: 1

Chapter/Section: Ch 06, Sec 01

Learning Objective: Solve systems of linear equations in two variables by graphing.

11) Solve the system of linear equations by graphing the following equations.

-2x - 6y = 14

-5x + 7y = -31

A) (-3, 2)

B) (2, -3)

C) (-2, -5)

D) (14, -31)

Diff: 2 Var: 1

Chapter/Section: Ch 06, Sec 01

Learning Objective: Solve systems of linear equations in two variables by graphing.

12) Solve the system of linear equations by graphing the following equations.

4x - 3y = 7

2x - 6y = 26

A) (-2, -5)

B) (-5, -2)

C) (5, -2)

D) (-2, 5)

Diff: 2 Var: 1

Chapter/Section: Ch 06, Sec 01

Learning Objective: Solve systems of linear equations in two variables by graphing.

13) Starbucks Coffee sells its House Blend for $9.52 per pound and its Sumatra coffee for $11.18 per pound. How many pounds of each type of coffee did a Starbucks outlet sell in one day if the total number of pounds sold was 60 and the day's receipts totaled $637.60? Let h represent the number of pounds of House Blend and s the number of pounds of Sumatra sold. Round your answer to the nearest pound.

A) h = 40 pounds, s = 20 pounds

B) h = 20 pounds, s = 40 pounds

C) h = 55 pounds, s = 5 pounds

D) h = 5 pounds, s = 55 pounds

Diff: 3 Var: 1

Chapter/Section: Ch 06, Sec 01

Learning Objective: Solve applications involving systems of linear equations.

14) A health food company mixes dried fruit with walnuts to make a trail mix blend. How many pounds of each ingredient must be mixed if dried fruit sells for $6.63 per pound, walnuts sell for $4.38 per pound, and the company produces 65 pounds per batch valued at $419.70? Let d represent the number of pounds of dried fruit and w the number of pounds of walnuts.

A) d = 15 pounds, w = 50 pounds

B) d = 50 pounds, w = 15 pounds

C) d = 5 pounds, w = 60 pounds

D) d = 60 pounds, w = 5 pounds

Diff: 3 Var: 1

Chapter/Section: Ch 06, Sec 01

Learning Objective: Solve applications involving systems of linear equations.

15) A catering company mixes cooked shredded beef with roasted Anaheim chilies to use as the filling in their house specialty burrito. How many pounds of both shredded beef that sells for$6.63 per pound and chilies that sell for $1.62 per pound must be mixed to produce 95 pounds of the mixture, witch sells for $454.50? Let b represent the number of pounds of beef and c represent the number of pounds of chilies.

A) b = 35 pounds, c = 60 pounds

B) b = 60 pounds, c = 35 pounds

C) b = 70 pounds, c = 25 pounds

D) b = 25 pounds, c = 70 pounds

Diff: 3 Var: 1

Chapter/Section: Ch 06, Sec 01

Learning Objective: Solve applications involving systems of linear equations.

16) Solve the system of linear equations by substitution.

7t - 2u = 39

2t + 6u = -48

Diff: 2 Var: 1

Chapter/Section: Ch 06, Sec 01

Learning Objective: Solve systems of linear equations in two variables using the substitution method.

17) Solve the system of linear equations by elimination.

-4j + 3k = 3

-3j - 3k = -45

Diff: 3 Var: 1

Chapter/Section: Ch 06, Sec 01

Learning Objective: Solve systems of linear equations in two variables using the elimination method.

18) A candy company mixes chocolate and peanuts to create one of their signature confections. How many pounds of chocolate costing $11.82 per pound must be mixed with peanuts costing $4.37 per pound to create 50 pounds of mixture that costs $330.25? Let c represent the number of pounds of chocolate and p represent the number of pounds of peanuts.

Diff: 3 Var: 1

Chapter/Section: Ch 06, Sec 01

Learning Objective: Solve applications involving systems of linear equations.

19) Solve the system of linear equations by substitution.

x - y = -30

x + y = -1

Diff: 3 Var: 1

Chapter/Section: Ch 06, Sec 01

Learning Objective: Solve systems of linear equations in two variables using the substitution method.

20) Solve the system of linear equations by elimination.

x - y = 13

x + y = -44

Diff: 3 Var: 1

Chapter/Section: Ch 06, Sec 01

Learning Objective: Solve systems of linear equations in two variables using the elimination method.

21) Solve the system of linear equations by elimination.

10z - 2w = -46

10z - 2w = 5

A) (10, 2)

B) (-46, 5)

C) infinite number of solutions

D) no solution

Diff: 2 Var: 1

Chapter/Section: Ch 06, Sec 01

Learning Objective: Solve systems of linear equations in two variables using the elimination method.

22) Solve the system of linear equations by elimination.

-4p - 8q = -64

-8p - 16q = -128

A) (6, 5)

B) (3, -3)

C) infinite number of solutions

D) no solution

Diff: 2 Var: 1

Chapter/Section: Ch 06, Sec 01

Learning Objective: Solve systems of linear equations in two variables using the elimination method.

23) Solve the system of linear equations by elimination.

2.3t - 3.3u = -19.78

2t + 2.1u = 17.09

Diff: 2 Var: 1

Chapter/Section: Ch 06, Sec 01

Learning Objective: Solve systems of linear equations in two variables using the elimination method.

24) Solve the system of linear equations by graphing the following equations.

-3x + 5y = -14

2x + 5y = -24

Diff: 2 Var: 1

Chapter/Section: Ch 06, Sec 01

Learning Objective: Solve systems of linear equations in two variables by graphing.

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