Chapter 6 review. 1. Which statement is true about the graphs of these equations?

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1 Name: Date: 1. Which statement is true about the graphs of these equations? y = 6x + 4 y = 5x 2 A. The lines intersect, but are not perpendicular. B. The lines are parallel. 4. Members of a senior class held a car wash to raise funds for their senior prom. They charged $3 to wash a car and $5 to wash a pick-up truck or a sport utility vehicle. If they earned a total of $275 by washing a total of 75 vehicles, how many cars did they wash? A. 25 B. 34 C. 45 D. 50 C. The lines are perpendicular. D. The lines coincide (same line). 2. Look at the following equations. 8p = 12 2q q + 4p = 6 5. What system of inequalities best represents the graph shown below? Which statement is true about the lines graphed from the equations? A. They coincide. B. They are parallel. C. They are perpendicular. D. They intersect but are not perpendicular. A. y > 2 and y > x + 1 B. y > 2 and y < x Marcy has a total of 100 dimes and quarters. If the total value of the coins is $14.05, how many quarters does she have? C. y < 2 and y > x + 1 D. y < 2 and y < x + 1 A. 27 B. 40 C. 56 D. 73 page 1

2 6. 9. A rectangle has a perimeter of 44 inches and an area of 72 square inches. What are the lengths of the 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 Which system of linear inequalities is represented by this graph? 10. The perimeter of a child s rectangular play yard is 64 yards. The length and width of the yard are consecutive odd integers. If the length (x) is the longer of the two dimensions, what is the width of the play yard? A. C. { y y x 2 { 2x y 3 x + y 2 B. D. { y 2x + 3 y x 2 { 2x + y 3 x y 2 A. 15 yards B. 17 yards C. 31 yards D. 33 yards 7. What is the solution to the following system of equations? { 2x 3y = 4 4x + y = 6 A. (5, 2) B. ( 2, 5) C. ( 1, 2) D. ( 2, 1) 11. Julia and Marcia bought identically priced cans of chili and identically priced jars of salsa to make a dip. Julia bought 3 cans of chili and 2 jars of salsa for $ Marcia bought 2 cans of chili and 4 jars of salsa for $ Which of the following systems of equations could be used to find x, the cost of one can of chili, and y, the cost of one jar of salsa? A. x + y = x + y = If 4 notebooks and 3 packages of pens cost $7.43 and 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 B x y = 11 x + y = 11 C. 2x + 4y = x + 3y = D. 3x + 2y = x + 4y = page 2

3 12. Use the system of inequalities to answer the question. y x + 1 y > 3x 2 Which graph shows the solution to this system of inequalities? 13. Two linear equations are given below. 2x 3y = 12 4x + 6y = 6 Which of the following statements about the equations is true? 14. The perimeter of a rectangle is 48 inches. The length of the rectangle is 3 times the width of the rectangle. What is the area of the rectangle? A. 24 square inches B. 54 square inches C. 108 square inches D. 432 square inches A. They represent the same line. B. They represent lines with negative slopes. C. They represent parallel lines. D. They represent perpendicular lines. page 3

4 15. Which of the following values of x and y are solutions of the system of inequalities shown below? x + 3y < 16 x + y > 10 A. x = 2; y = 8 B. x = 9; y = 2 C. x = 1; y = 5 D. x = 7; y = What is the value of x in the solution to the following system of equations? 19. A telephone company offers customers two payment plans for monthly service. Plan A costs $5 per month plus $0.10 per minute for calls. Plan B costs $8 per month plus $0.07 per minute for calls. a) How many minutes of calls would it take for Plan A and Plan B to cost the same? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation. x + y = 5 2x + 6y = 22 A. x = 4 B. x = 3 C. x = 2 D. x = The only coins that Alexis has are dimes and quarters. Her coins have a total value of $5.80. She has a total of 40 coins. Which of the following systems of equations can be used to find the number of dimes, d, and the number of quarters, q, that Alexis has? A. d + q = d + 40q = 5.80 B. d + q = d q = 40 C. d + q = d q = 40 D. d + q = d q = The Sanchez family is planning a trip to an amusement park. The park has two ticket plans. Plan A offers a weekend pass for $12 plus $0.50 per ride. Plan B is $1.25 for each ride. Let x represent the number of rides each person will ride and y represent the cost per person, in dollars. Which of these systems of equations could be used to choose a ticket plan? A. y = 0.50x + 12 y = 1.25x C. y = 0.50x y = 1.25x B. y = 12x y = x D. y = x + 12 y = x Luke has 15 coins. He has only nickels and dimes. If the total value of the coins is $1.20, how many nickels does he have? A. 5 B. 6 C. 8 D. 9 page 4

5 21. Look at the system of equations below. y = 3x + 2 y = 2x 3 Which of these graphs represents this system of equations? 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 park ranger 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 month of July. He earned $3,600. Russ earned $25 per hour each weekday that he worked. He earned $40 per hour each Saturday that he worked. Let x represent the number of weekday hours worked and y represent the number of Saturday hours worked. Which system of equations represents this situation? A. x + y = x + 40y = 3, 600 B. x + y = x + 25y = 3, 600 C. x + y = 3, x + 40y = 135 D. x + y = 3, x + 25y = 135 page 5

6 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 to work to earn the same amount of money at Job B as at Job A? 26. The graph for the system of inequalities without the shading of its solution set is shown on the coordinate grid. 2x + y < 1 3x y < 5 A. 40 B. 41 C. 420 D The graph of the system of equations 2y = 4x + 6 x = 2 is shown below. Which area should be shaded to represent the solution set of this system of inequalities? A. Area 1 B. Area 2 C. Area 3 D. Area Angela graphed the following two linear equations on a coordinate grid. Which point satisfies both of the following inequalities? 2y 4x + 6 x 2 A. (3, 1) B. ( 1, 3) C. (1, 3) D. (1, 3) 2x + 3y = 4 4x + 6y = 7 Which of these best describes the graph of the two 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. page 6

7 28. Two lines in a coordinate plane have no points of intersection. Which of these could be the equations of the lines? A. 4x + 2y = 6 10x + 5y = 7 C. 4x + 2y = 6 5x 10y = 6 B. 4x + 2y = 6 10x + 5y = 15 D. 5x + 10y = 6 5x 10y = Which graph best represents the solution to the system of linear inequalities below? x + y 5 2x + 3y 6 page 7

8 30. Which of the following graphs best represents the solution set to the system of linear inequalities shown below? 3x 5y 15 2x + 3y > 6 page 8

9 31. Which of the following graphs best represents the solution of the system of linear equations shown below? y = x + 4 3x + y = Given: 33. Given the system of equations: 6x 3y = 42 4x + 2y = 4 6x + y = 9.7 4x + 2y = 9.8 What is x + y? What is the value of x? A. 6 B. 5 C. 4 D. 9 A. 1.0 B. 1.2 C. 1.9 D. 2.5 page 9

10 34. A group of 3 children and 2 adults pay a total of $120 to take a karate class. A group of 5 children and 1 adult take the same karate class for $95. What is the total cost for 1 child and 1 adult to take the karate class? A. $60 B. $55 C. $51 D. $ Josh and Andrea each have $ Josh spends all his money and buys 2 hamburgers and 3 sodas. Andrea spends $7.50 and buys 2 hamburgers and one soda. What is the cost of one hamburger? A. $1.50 B. $2.50 C. $3.00 D. $ Which graph represents the system of inequalities below? 2x 3y 9 4x + 2y < 8 page 10