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