Download Accelerated Algebra Chapter 5 Study Guide

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Class: _________________
Date: _________
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Accelerated Algebra Chapter 5 Study Guide
Short Answer
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely
many solutions. If the system has one solution, name it.
1. y = −x + 5
y = 6x − 2
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ID: A
2. −4x + y = 2
−4x − 5 =
y
2
Use substitution to solve the system of equations.
3. y = x + 1
8x − 4y = 0
4. −9 = x − 3y
−2x + 6 = 6y
5. The sum of two numbers is 90. Their difference is 12. What are the numbers?
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Name: ______________________
ID: A
6. At a local electronics store, CDs were on sale. Some were priced at $14.00 and some at $12.00. Sabrina
bought 9 CDs and spent a total of $114.00. How many $12.00 CDs did she purchase?
7. Angle A and angle B are complementary, that is their measurements add up to 90°. Angle B measures 32°
more than angle A. What are the measurements of the two angles?
8. Reid and Maria both play soccer. This season, Reid scored 4 less than twice the number of goals that Maria
scored. The difference in the number of goals they scored was 6. How many goals did each of them score?
9. Mrs. Davis went to a produce market to buy bananas and strawberries. She spent $8.00. If the bananas were
$0.50 per pound, and the strawberries were 4 times that much, how many pounds of bananas did she buy if she
bought 7 pounds of fruit altogether?
Use elimination to solve the system of equations.
10. −2x − 10y = 10
−3x + 10y = −10
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Name: ______________________
ID: A
11. −8x + 8y = −8
−8x + 4y = 8
12. 5x − 2y = −3
4x − 2y = −6
13. −3x − 2y = −5
7x + 6y = 1
14. −4x − 6y = −6
7x + 9y = −9
15. Isaac downloaded 7 ringtones. Each polyphonic ringtone costs $3.25, and each standard ringtone costs $1.50.
If he spends a total of $21 on ringtones, find the number of polyphonic and standard ringtones he
downloaded.
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Name: ______________________
ID: A
16. Christie has a total of 15 pieces of fruit, all bananas and apples, worth $1.59. Bananas are 13 cents each and
apples are 7 cents each. How many bananas and how many apples does she have?
Determine the best method to solve the system of equations. Then solve the system.
17. 7x − 2y = 8
5x + 2y = 4
18. x = 2y − 1
3x − 3y = 9
19. −5x + 3y = −18
2x + 2y = 4
20. x = −y
5x + 6y = −3
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Name: ______________________
21.
22.
5
6
x+ 3 y = 4
1
6
x+ 3 y = 0
1
4
x+ 4 y = 1
ID: A
2
2
3
2x + 6y = 8
23. How many grams of pure silver and how many grams of an alloy that is 65% silver should be melted together
to produce 56g of an alloy that is 80% silver?
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Name: ______________________
ID: A
24. Five times one number added to another number is 32. Three times the first number minus the other number
is 8. Find the numbers.
25. Six times a number plus five times another number equals 56. The sum of the two numbers is 10. What are the
numbers?
26. A boat travels 33 miles downstream in 4 hours. The return trip takes the boat 7 hours. Find the speed of the
boat in still water.
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ID: A
Accelerated Algebra Chapter 5 Study Guide
Answer Section
SHORT ANSWER
1. one solution; (1, 4)
2. one solution; (–1, –2)
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
(1, 2)
(–3, 2)
39 and 51
6
29° and 61°
Reid scored 16 and Maria scored 10.
4 pounds
(0, –1)
(–3, –4)
(3, 9)
(7, –8)
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ID: A
14. (–18, 13)
15. 6 polyphonic, 1 standard
16. 9 bananas, 6 apples
Ê
1 ˆ
17. elimination using addition; ÁÁÁÁ 1, − 2 ˜˜˜˜
Ë
¯
18. substitution; (7, 4)
19. elimination using multiplication; (3, − 1)
20. substitution; (3, − 3)
Ê
3 ˆ
21. elimination using subtraction; ÁÁÁÁ 6, − 2 ˜˜˜˜
Ë
¯
22. elimination using multiplication; infinitely many solutions
23. 24g of pure silver and 32g of a 65% alloy
x + y = 56
x + 0.65y = 0.80 ( 56 )
Substitute 56 − y for x in the second equation and solve for y. Substitute that value into the first equation and
solve for x.
24. 5, 7
5x + y = 32
3x − y = 8
Eliminate one variable by adding the two equations. Solve for x and then substitute that value into one of the
equations to find the value of y.
25. 6, 4
6x + 5y = 56
x + y = 10
Eliminate the y terms by first multiplying the second equation by 5 and then subtracting the two equations.
Solve for x and then substitute that value into one of the equations to find the value of y.
26. 6.48 mph
4x + 4y = 33
7x − 7y = 33
Eliminate the x terms by first multiplying the top equation by 7 and the bottom one by 4 and then subtracting
the two equations. Solve for y and then substitute that value into one of the equations to find the value of x.
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