Chapter 6 review

Name: Date:

1. Which statement is true about the graphs of theseequations?

y = 6x + 4y = 5x − 2

A. The lines intersect, but are not perpendicular.

B. The lines are parallel.

C. The lines are perpendicular.

D. The lines coincide (same line).

2. Look at the following equations.

8p = 12 − 2qq + 4p = 6

Which statement is true about the lines graphedfrom the equations?

A. They coincide.

B. They are parallel.

C. They are perpendicular.

D. They intersect but are not perpendicular.

3. Marcy has a total of 100 dimes and quarters. Ifthe total value of the coins is $14.05, how manyquarters does she have?

A. 27 B. 40 C. 56 D. 73

4. Members of a senior class held a car wash to raisefunds for their senior prom. They charged $3 towash a car and $5 to wash a pick-up truck or asport utility vehicle. If they earned a total of $275by washing a total of 75 vehicles, how many carsdid they wash?

A. 25 B. 34 C. 45 D. 50

5. What system of inequalities best represents thegraph shown below?

A. y > −2 and y > x + 1

B. y > −2 and y < x + 1

C. y < −2 and y > x + 1

D. y < −2 and y < x + 1

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Which system of linear inequalities is representedby this graph?

A.

{y ≥ 1

2 + 3

y ≥ x − 2B.

{y ≥ 2x + 3y ≤ x − 2

C.

{2x − y ≥ 3x + y ≤ 2

D.

{2x + y ≥ 3x − y ≥ 2

7. What is the solution to the following system ofequations?{

2x − 3y = 44x + y = −6

A. (5,−2) B. (−2, 5)

C. (−1,−2) D. (−2,−1)

8. If 4 notebooks and 3 packages of pens cost $7.43and 5 notebooks and 2 packages of pens cost$7.03, what is the cost of 1 notebook?

A. $0.89 B. $0.79 C. $1.29 D. $1.09

9. A rectangle has a perimeter of 44 inches and anarea of 72 square inches. What are the lengths ofthe sides of the rectangle?

A. 2 inches and 36 inches

B. 4 inches and 18 inches

C. 8 inches and 9 inches

D. 11 inches and 11 inches

10. The perimeter of a child’s rectangular play yard is64 yards. The length and width of the yard areconsecutive odd integers. If the length (x) is thelonger of the two dimensions, what is the width ofthe play yard?

A. 15 yards B. 17 yards

C. 31 yards D. 33 yards

11. Julia and Marcia bought identically priced cans ofchili and identically priced jars of salsa to make adip.

• Julia bought 3 cans of chili and 2 jars ofsalsa for $10.07.

• Marcia bought 2 cans of chili and 4 jarsof salsa for $12.98.

Which of the following systems of equations couldbe used to find x, the cost of one can of chili, andy, the cost of one jar of salsa?

A. x + y = 10.07x + y = 12.98

B. 10.07x + 12.98y = 11x + y = 11

C. 2x + 4y = 10.072x + 3y = 12.98

D. 3x + 2y = 10.072x + 4y = 12.98

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12. Use the system of inequalities to answer the question.

y ≤ x + 1y > −3x − 2

Which graph shows the solution to this system of inequalities?

A. B.

C. D.

13. Two linear equations are given below.

2x − 3y = 12−4x + 6y = 6

Which of the following statements about theequations is true?

A. They represent the same line.

B. They represent lines with negative slopes.

C. They represent parallel lines.

D. They represent perpendicular lines.

14. The perimeter of a rectangle is 48 inches. Thelength of the rectangle is 3 times the width of therectangle. What is the area of the rectangle?

A. 24 square inches B. 54 square inches

C. 108 square inches D. 432 square inches

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15. Which of the following values of x and y aresolutions of the system of inequalities shownbelow?

x + 3y < 16x + y > 10

A. x = 2; y = 8 B. x = 9; y = 2

C. x = 1; y = 5 D. x = 7; y = 2

16. What is the value of x in the solution to thefollowing system of equations?

x + y = 52x + 6y = 22

A. x = 4 B. x = 3 C. x = 2 D. x = 1

17. The only coins that Alexis has are dimes andquarters.

• Her coins have a total value of $5.80.

• She has a total of 40 coins.

Which of the following systems of equations canbe used to find the number of dimes, d, and thenumber of quarters, q, that Alexis has?

A. d + q = 5.8040d + 40q = 5.80

B. d + q = 405.80d + 5.80q = 40

C. d + q = 5.800.10d + 0.25q = 40

D. d + q = 400.10d + 0.25q = 5.80

18. Luke has 15 coins. He has only nickels anddimes. If the total value of the coins is $1.20,how many nickels does he have?

A. 5 B. 6 C. 8 D. 9

19. A telephone company offers customers twopayment plans for monthly service.

Plan A costs $5 per month plus $0.10 per minutefor calls.

Plan B costs $8 per month plus $0.07 per minutefor calls.

a) How many minutes of calls would it take forPlan A and Plan B to cost the same? Usemathematics to explain how you determinedyour answer. Use words, symbols, or both inyour explanation.

20. The Sanchez family is planning a trip to anamusement park. The park has two ticket plans.

Plan A offers a weekend pass for $12 plus $0.50per ride.

Plan B is $1.25 for each ride.

Let x represent the number of rides each personwill ride and y represent the cost per person, indollars. Which of these systems of equationscould be used to choose a ticket plan?

A. y = 0.50x + 12y = 1.25x

B. y = 12x + 0.50y = x + 1.25

C. y = 0.50xy = 1.25x

D. y = x + 12y = x + 1.25

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21. Look at the system of equations below.

y = −3x + 2y = 2x − 3

Which of these graphs represents this system of equations?

A. B.

C. D.

22. A park ranger spent $208 to buy 12 trees.Redwood trees cost $24 each and spuce trees cost$16 each. How many of each tree did the parkranger buy?

A. 10 redwoods and 2 spruce

B. 9 redwoods and 3 spruce

C. 3 redwoods and 9 spruce

D. 2 redwoods and 10 spruce

23. Russ worked a total of 135 hours during the monthof July. He earned $3,600. Russ earned $25 perhour each weekday that he worked. He earned$40 per hour each Saturday that he worked. Letx represent the number of weekday hours workedand y represent the number of Saturday hoursworked. Which system of equations represents thissituation?

A. x + y = 13525x + 40y = 3, 600

B. x + y = 13540x + 25y = 3, 600

C. x + y = 3, 60025x + 40y = 135

D. x + y = 3, 60040x + 25y = 135

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24. Mary is considering two job offers. Job A pays$8.00 an hour and offers a one-time $100 bonus.Job B pays $8.50 an hour and offers a one-time$80 bonus. How many hours would Mary have towork to earn the same amount of money at Job Bas at Job A?

A. 40 B. 41 C. 420 D. 428

25. The graph of the system of equations

2y = −4x + 6x = 2

is shown below.

Which point satisfies both of the followinginequalities?

2y ≥ −4x + 6x ≤ 2

A. (3,−1) B. (−1, 3)

C. (1, 3) D. (1,−3)

26. The graph for the system of inequalities withoutthe shading of its solution set is shown on thecoordinate grid.

2x + y < 13x − y < −5

Which area should be shaded to represent thesolution set of this system of inequalities?

A. Area 1 B. Area 2

C. Area 3 D. Area 4

27. Angela graphed the following two linear equationson a coordinate grid.

2x + 3y = 44x + 6y = 7

Which of these best describes the graph of thetwo linear equations?

A. The two lines are parallel.

B. The two lines are perpendicular.

C. The two lines have the same graph.

D. The two lines intersect at only one point.

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28. Two lines in a coordinate plane have no pointsof intersection. Which of these could be theequations of the lines?

A. 4x + 2y = 610x + 5y = 7

B. 4x + 2y = 610x + 5y = 15

C. 4x + 2y = 65x − 10y = 6

D. 5x + 10y = 65x − 10y = 6

29. Which graph best represents the solution to the system of linear inequalities below?

x + y ≤ 5−2x + 3y ≥ 6

A. B.

C. D.

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30. Which of the following graphs best represents the solution set to the system of linear inequalities shown below?

3x − 5y ≤ 152x + 3y > −6

A. B.

C. D.

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31. Which of the following graphs best represents the solution of the system of linear equations shown below?

y = x + 43x + y = −8

A. B.

C. D.

32. Given:

6x − 3y = 424x + 2y = −4

What is x + y?

A. −6 B. −5 C. 4 D. 9

33. Given the system of equations:

6x + y = 9.74x + 2y = 9.8

What is the value of x?

A. 1.0 B. 1.2 C. 1.9 D. 2.5

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34. A group of 3 children and 2 adults pay a total of$120 to take a karate class. A group of 5 childrenand 1 adult take the same karate class for $95.What is the total cost for 1 child and 1 adult totake the karate class?

A. $60 B. $55 C. $51 D. $48

35. Josh and Andrea each have $10.50. Josh spendsall his money and buys 2 hamburgers and 3 sodas.Andrea spends $7.50 and buys 2 hamburgers andone soda. What is the cost of one hamburger?

A. $1.50 B. $2.50 C. $3.00 D. $8.75

36. Which graph represents the system of inequalities below?

2x − 3y ≥ 94x + 2y < 8

A. B.

C. D.

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