Practice Test - Chapter 6
Graph each system and determine the number of solutions that it has. If it has one solution, name it.
1. y = 2x
y =6 −x
ANSWER: one; (2, 4)
2. y = x − 3
y = −2x + 9
ANSWER: one; (4, 1)
3. x − y = 4
x + y = 10
ANSWER: one; (7, 3)
4. 2x + 3y = 4
2x + 3y = −1
ANSWER: no solution
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Practice Test - Chapter 6
4. 2x + 3y = 4
2x + 3y = −1
ANSWER: no solution
Use substitution to solve each system of equations.
5. y = x + 8
2x + y = −10
ANSWER: (−6, 2)
6. x = −4y − 3
3x − 2y = 5
ANSWER: (1, −1)
7. GARDENING Corey has 42 feet of fencing around his garden. The garden is rectangular in shape, and its length is
equal to twice the width minus 3 feet. Define the variables, and write a system of equations to find the length and
width of the garden. Solve the system by using substitution.
ANSWER: Sample answer: Let w be the width and let
be the length; 2w + 2
= 42,
= 2w − 3; w = 8 ft,
= 13 ft
8. MULTIPLE CHOICE Use elimination to solve the system.
6x − 4y = 6
−6x + 3y = 0
A (5, 6)
B (−3, −6)
C (1, 0)
D (4, −8)
ANSWER: B
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9. SHOPPING Shelly has $175 to shop for jeans and sweaters. Each pair of jeans costs $25, each sweater costs $20,
and she buys 8 items. Determine the number of pairs of jeans and sweaters Shelly bought.
ANSWER: Practice
Test - Chapter 6
Sample answer: Let w be the width and let
be the length; 2w + 2
= 42,
= 2w − 3; w = 8 ft,
= 13 ft
8. MULTIPLE CHOICE Use elimination to solve the system.
6x − 4y = 6
−6x + 3y = 0
A (5, 6)
B (−3, −6)
C (1, 0)
D (4, −8)
ANSWER: B
9. SHOPPING Shelly has $175 to shop for jeans and sweaters. Each pair of jeans costs $25, each sweater costs $20,
and she buys 8 items. Determine the number of pairs of jeans and sweaters Shelly bought.
ANSWER: 3 jeans, 5 sweaters
Use elimination to solve each system of equations.
10. x + y = 13
x −y = 5
ANSWER: (9, 4)
11. 3x + 7y = 2
3x − 4y = 13
ANSWER: (3, −1)
12. x + y = 8
x − 3y = −4
ANSWER: (5, 3)
13. 2x + 6y = 18
3x + 2y = 13
ANSWER: (3, 2)
14. MAGAZINES Julie subscribes to a sports magazine and a fashion magazine. She received 24 issues this year. The
number of fashion issues is 6 less than twice the number of sports issues. Define the variables, and write a system of
equations to find the number of issues of each magazine.
ANSWER: Let f = the number of fashion magazines and s = the number of sports magazines. Then f + s = 24, and f = 2s - 6. So
s = 10 and f = 14.
Determine the best method to solve each system of equations. Then solve the system.
15. y = 3x
x + 2y = 21
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ANSWER: Substitution; (3, 9)
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equations to find the number of issues of each magazine.
ANSWER: Let f Test
= the -number
of 6fashion magazines and s = the number of sports magazines. Then f + s = 24, and f = 2s - 6. So
Practice
Chapter
s = 10 and f = 14.
Determine the best method to solve each system of equations. Then solve the system.
15. y = 3x
x + 2y = 21
ANSWER: Substitution; (3, 9)
16. x + y = 12
y =x−4
ANSWER: Substitution; (8, 4)
17. x + y = 15
x −y = 9
ANSWER: Elimination (+); (12, 3)
18. 3x + 5y = 7
2x − 3y = 11
ANSWER: Elim. (×); (4, −1)
19. OFFICE SUPPLIES At a sale, Ricardo bought 24 reams of paper and 4 inkjet cartridges for $320. Britney bought
2 reams of paper and
1 inkjet cartridge for $50. The reams of paper were all the same price and the inkjet cartridges were all the same
price. Write a system of
equations to represent this situation. Determine the best method to solve the system of equations. Then solve the
system.
ANSWER: 24p + 4c = 320
2p + c = 50
Substitution;
paper, $7.50 per ream, cartridge, $35 each
Solve each system of inequalities by graphing.
20. x > 2
y <4
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21. x + y ≤ 5
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24p + 4c = 320
2p + c = 50
Substitution;
Practice
Test - Chapter 6
paper, $7.50 per ream, cartridge, $35 each
Solve each system of inequalities by graphing.
20. x > 2
y <4
ANSWER: 21. x + y ≤ 5
y ≥ x + 2
ANSWER: 22. 3x − y > 9
y > −2x
ANSWER: 23. y ≥ 2x + 3
−4x − 3y > 12
ANSWER: eSolutions Manual - Powered by Cognero
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Practice Test - Chapter 6
23. y ≥ 2x + 3
−4x − 3y > 12
ANSWER: eSolutions Manual - Powered by Cognero
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