Name: ________________________ Class: ___________________ Date: __________

ID: A

Chapter 7: Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. ____

1. Which linear system has the solution x = –2 and y = 6? a. x + 3y = 16 c. x + 2y = –2 4x + 4y = 16 2x + 4y = –4 b. x + 3y = 17 d. 2x + y = –2 2x + y = 15 x + y = 16

____

2. Create a linear system to model this situation: A collection of nickels and dimes contains four times as many dimes as nickels. The total value of the collection is $20.25. a. d = 4n b. d = 4n c. n = 4d d. d + n = 15 5n + 10d = 2025 5n + 10d = 2025 5d + 10n = 2025 5n + 10d = 2025

____

3. Create a linear system to model this situation: A woman is 3 times as old as her son. In thirteen years, she will be 2 times as old as her son will be. a. w = s + 3 c. w = 3s w + 13 = 2s w = 2s b. w = 3s d. w = 3s w + 13 = 2(s + 13) s + 13 = 2(w + 13)

____

4. Create a linear system to model this situation: Tickets for a school play cost $8 for adults and $4.75 for students. There were ten more student tickets sold than adult tickets, and a total of $1399 in ticket sales was collected. a. 8a + 4.75s = 1399 c. 8a + 4.75s = 1399 s = a + 10 a = s + 10 b. 8a + 4.75s = 1399 d. 4.75a + 8s = 1399 a + s = 10 s = a + 10

____

5. Write an equivalent system with integer coefficients. 3 5x + y = 14 2 5 755 x + 5y = 6 6 a. b.

10x + 3y = 1 5x + 30y = 1 3x + 10y = 28 5x + 30y = 755

c. d.

1

10x + 3y = 28 30x + 5y = 755 10x + 3y = 28 5x + 30y = 755

Name: ________________________ ____

6. Which graph represents the solution of the linear system: –3x – y = –5 4x – y = 2

a. b. ____

ID: A

Graph A Graph B

c. d.

Graph C Graph D

7. Determine the number of solutions of the linear system: 14x – 5y = 123 14x – 5y = 73 a. b.

no solution infinite solutions

c. d.

2

two solutions one solution

Name: ________________________ ____

8. Determine the number of solutions of the linear system: 14x + 7y = 315 16x – 2y = 610 a. b.

____

ID: A

no solution one solution

c. d.

two solutions infinite solutions

9. Which linear system is represented by this graph? a) x – y = 3 6x + 5y = 14 b) x + y = 5 6x + 5y = 14 c) x + y = 7 7x + 5y = 14 d) x + y = 9 5x + 6y = 14

a.

System a

b.

System b

c.

System c

d.

System d

____ 10. The first equation of a linear system is 2x + 3y = 52. Choose a second equation to form a linear system with infinite solutions. i) 2x + 3y = –260 ii) –10x – 15y = –260 iii) –10x + 3y = –260 iv) –10x + 3y = 255 a.

Equation iii

b.

Equation iv

c.

3

Equation i

d.

Equation ii

Name: ________________________

ID: A

____ 11. Determine the number of solutions of the linear system: 5x + 7y = 76 –25x – 35y = –380 a. b.

2 solutions one solution

c. d.

infinite solutions no solution

____ 12. The first equation of a linear system is 8x + 13y = 166. Choose a second equation to form a linear system with exactly one solution. i) 8x + 13y = –830 ii) –40x – 65y = –830 iii) –40x + 13y = –830 iv) –40x – 65y = 0 a.

Equation iii

b.

Equation i

c.

Equation ii

d.

Equation iv

System a

d.

System c

____ 13. Which linear system is represented by this graph? a) x – y = 5 5x + 6y = 18 b) x – y = 7 5x + 6y = 18 c) x – y = 9 6x + 6y = 18 d) x – y = 11 6x + 5y = 18

a.

System d

b.

System b

c.

4

Name: ________________________

ID: A

____ 14. The first equation of a linear system is –6x + 12y = –42. Choose a second equation to form a linear system with no solution. i) –6x + 12y = 126 ii) 18x – 36y = 126 iii) 18x + 12y = 126 iv) 18x + 36y = 0 a.

Equation iv

b.

Equation ii

c.

Equation iii

d.

Equation i

____ 15. Two lines in a linear system have the same slope, but different y-intercepts. How many solutions does the linear system have? a. b.

two solutions no solution

c. d.

infinite solutions one solution

Short Answer 16. Create a linear system to model this situation: Two ships start sailing towards each other at the same time from two islands that are 365 km apart. One ship travels 5 km/h faster than the other. They meet in 5 h. What is the average speed of each ship? Verify that 34 km/h and 39 km/h represent the solution of the linear system.

17. Solve this linear system by graphing. –3x – 2y = 16 –x + y = –8

5

Name: ________________________

ID: A

18. Solve this linear system by graphing. y = –8 –3x + y = 7

19. Use substitution to solve this linear system: 8x + y = −458 −5x + 3y = 221 . . .

20. Use an elimination strategy to solve this linear system. 12c + 28d = 12 −20c + 16d = 168 . . . .

6

Name: ________________________

ID: A

21. For what values of k does the linear system below have: a) infinite solutions? b) one solution? c) no solution? 2 x + y = 16 3 kx + 3y = 48 . . .

22. Use the graph to solve the linear system: y = –5x − 2 y + 2 = 2x

23. Use substitution to solve this linear system. x = 2y – 56 5x + 13y = 410 . . .

24. Use substitution to solve this linear system. x=4+y 4x + 16y = –264

7

Name: ________________________

ID: A

25. Use substitution to solve this problem: The perimeter of a rectangular field is 276 m. The length is 18 m longer than the width. What are the dimensions of the field? . . .

26. Use an elimination strategy to solve this linear system. 4x − 3y = 10 2x + 5y = 18 . . .

27. Use an elimination strategy to solve this linear system. 3x − 2y = 5 2x + 7y = 20 . . .

28. Use an elimination strategy to solve this linear system. 3 2 m + n = 16 3 4 1 3 − m + n = 18 2 8 . . .

29. Use an elimination strategy to solve this linear system. 20x − 24y = −52 8x + 32y = 104 . . .

8

ID: A

Chapter 7: Practice Test Answer Section MULTIPLE CHOICE 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

A A B A D A A B A D C A C D B

SHORT ANSWER 16. Let x represent the speed of the slower ship and y represent the speed of the faster ship. A linear system is: x+5=y 5x + 5y = 365 Since x = 34 and y = 39 satisfy each equation, these numbers are the solution of the linear system.

1

ID: A 17. (0, –8)

18. (–5, –8)

19. x = –55; y = –18 20. c = −6 d=3 21. a) k = 2 b) k ≠ 2 c) For the system to have no solution, the lines must be parallel; that is, their slopes are equal and their y-intercepts are different. But the lines have the same y-intercept, so they cannot be parallel. 22. (0, –2) 2

ID: A 23. 24. 25. 26. 27. 28. 29.

(4, 30) (–10, –14) 78 m by 60 m x = 4 and y = 2 x = 3 and y = 2 m = −12 and n = 32 x = 1 and y = 3

3

ID: A

Chapter 7: Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. ____

1. Which linear system has the solution x = –2 and y = 6? a. x + 3y = 16 c. x + 2y = –2 4x + 4y = 16 2x + 4y = –4 b. x + 3y = 17 d. 2x + y = –2 2x + y = 15 x + y = 16

____

2. Create a linear system to model this situation: A collection of nickels and dimes contains four times as many dimes as nickels. The total value of the collection is $20.25. a. d = 4n b. d = 4n c. n = 4d d. d + n = 15 5n + 10d = 2025 5n + 10d = 2025 5d + 10n = 2025 5n + 10d = 2025

____

3. Create a linear system to model this situation: A woman is 3 times as old as her son. In thirteen years, she will be 2 times as old as her son will be. a. w = s + 3 c. w = 3s w + 13 = 2s w = 2s b. w = 3s d. w = 3s w + 13 = 2(s + 13) s + 13 = 2(w + 13)

____

4. Create a linear system to model this situation: Tickets for a school play cost $8 for adults and $4.75 for students. There were ten more student tickets sold than adult tickets, and a total of $1399 in ticket sales was collected. a. 8a + 4.75s = 1399 c. 8a + 4.75s = 1399 s = a + 10 a = s + 10 b. 8a + 4.75s = 1399 d. 4.75a + 8s = 1399 a + s = 10 s = a + 10

____

5. Write an equivalent system with integer coefficients. 3 5x + y = 14 2 5 755 x + 5y = 6 6 a. b.

10x + 3y = 1 5x + 30y = 1 3x + 10y = 28 5x + 30y = 755

c. d.

1

10x + 3y = 28 30x + 5y = 755 10x + 3y = 28 5x + 30y = 755

Name: ________________________ ____

6. Which graph represents the solution of the linear system: –3x – y = –5 4x – y = 2

a. b. ____

ID: A

Graph A Graph B

c. d.

Graph C Graph D

7. Determine the number of solutions of the linear system: 14x – 5y = 123 14x – 5y = 73 a. b.

no solution infinite solutions

c. d.

2

two solutions one solution

Name: ________________________ ____

8. Determine the number of solutions of the linear system: 14x + 7y = 315 16x – 2y = 610 a. b.

____

ID: A

no solution one solution

c. d.

two solutions infinite solutions

9. Which linear system is represented by this graph? a) x – y = 3 6x + 5y = 14 b) x + y = 5 6x + 5y = 14 c) x + y = 7 7x + 5y = 14 d) x + y = 9 5x + 6y = 14

a.

System a

b.

System b

c.

System c

d.

System d

____ 10. The first equation of a linear system is 2x + 3y = 52. Choose a second equation to form a linear system with infinite solutions. i) 2x + 3y = –260 ii) –10x – 15y = –260 iii) –10x + 3y = –260 iv) –10x + 3y = 255 a.

Equation iii

b.

Equation iv

c.

3

Equation i

d.

Equation ii

Name: ________________________

ID: A

____ 11. Determine the number of solutions of the linear system: 5x + 7y = 76 –25x – 35y = –380 a. b.

2 solutions one solution

c. d.

infinite solutions no solution

____ 12. The first equation of a linear system is 8x + 13y = 166. Choose a second equation to form a linear system with exactly one solution. i) 8x + 13y = –830 ii) –40x – 65y = –830 iii) –40x + 13y = –830 iv) –40x – 65y = 0 a.

Equation iii

b.

Equation i

c.

Equation ii

d.

Equation iv

System a

d.

System c

____ 13. Which linear system is represented by this graph? a) x – y = 5 5x + 6y = 18 b) x – y = 7 5x + 6y = 18 c) x – y = 9 6x + 6y = 18 d) x – y = 11 6x + 5y = 18

a.

System d

b.

System b

c.

4

Name: ________________________

ID: A

____ 14. The first equation of a linear system is –6x + 12y = –42. Choose a second equation to form a linear system with no solution. i) –6x + 12y = 126 ii) 18x – 36y = 126 iii) 18x + 12y = 126 iv) 18x + 36y = 0 a.

Equation iv

b.

Equation ii

c.

Equation iii

d.

Equation i

____ 15. Two lines in a linear system have the same slope, but different y-intercepts. How many solutions does the linear system have? a. b.

two solutions no solution

c. d.

infinite solutions one solution

Short Answer 16. Create a linear system to model this situation: Two ships start sailing towards each other at the same time from two islands that are 365 km apart. One ship travels 5 km/h faster than the other. They meet in 5 h. What is the average speed of each ship? Verify that 34 km/h and 39 km/h represent the solution of the linear system.

17. Solve this linear system by graphing. –3x – 2y = 16 –x + y = –8

5

Name: ________________________

ID: A

18. Solve this linear system by graphing. y = –8 –3x + y = 7

19. Use substitution to solve this linear system: 8x + y = −458 −5x + 3y = 221 . . .

20. Use an elimination strategy to solve this linear system. 12c + 28d = 12 −20c + 16d = 168 . . . .

6

Name: ________________________

ID: A

21. For what values of k does the linear system below have: a) infinite solutions? b) one solution? c) no solution? 2 x + y = 16 3 kx + 3y = 48 . . .

22. Use the graph to solve the linear system: y = –5x − 2 y + 2 = 2x

23. Use substitution to solve this linear system. x = 2y – 56 5x + 13y = 410 . . .

24. Use substitution to solve this linear system. x=4+y 4x + 16y = –264

7

Name: ________________________

ID: A

25. Use substitution to solve this problem: The perimeter of a rectangular field is 276 m. The length is 18 m longer than the width. What are the dimensions of the field? . . .

26. Use an elimination strategy to solve this linear system. 4x − 3y = 10 2x + 5y = 18 . . .

27. Use an elimination strategy to solve this linear system. 3x − 2y = 5 2x + 7y = 20 . . .

28. Use an elimination strategy to solve this linear system. 3 2 m + n = 16 3 4 1 3 − m + n = 18 2 8 . . .

29. Use an elimination strategy to solve this linear system. 20x − 24y = −52 8x + 32y = 104 . . .

8

ID: A

Chapter 7: Practice Test Answer Section MULTIPLE CHOICE 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

A A B A D A A B A D C A C D B

SHORT ANSWER 16. Let x represent the speed of the slower ship and y represent the speed of the faster ship. A linear system is: x+5=y 5x + 5y = 365 Since x = 34 and y = 39 satisfy each equation, these numbers are the solution of the linear system.

1

ID: A 17. (0, –8)

18. (–5, –8)

19. x = –55; y = –18 20. c = −6 d=3 21. a) k = 2 b) k ≠ 2 c) For the system to have no solution, the lines must be parallel; that is, their slopes are equal and their y-intercepts are different. But the lines have the same y-intercept, so they cannot be parallel. 22. (0, –2) 2

ID: A 23. 24. 25. 26. 27. 28. 29.

(4, 30) (–10, –14) 78 m by 60 m x = 4 and y = 2 x = 3 and y = 2 m = −12 and n = 32 x = 1 and y = 3

3