1. Chapter 7: Practice Test. Multiple Choice. Identify the choice that best
completes the statement or answers the question. ____ 1. Which linear system
has the ...
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
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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)
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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
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5. Write an equivalent system with integer coefficients. 3 5x + y = 14 2 5 755 x + 5y = 6 6 a. b.
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 . . .
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
