Name
Class
Date
Extra Practice
Chapter 6
Lesson 6-1
Solve each system by graphing.
1. x– y = 7
2. y = 2x + 3
3. y = –2x + 6
3x + 2y = 6
3x + 4y = 24
Write and solve a system of equations by graphing.
4. One calling card has a $.50 connection fee and charges $.02 per minute.
Another card has a $.25 connection fee and charges $.03 per minute.
After how many minutes would a call cost the same amount using either
card?
5. Suppose that you have $75 in your savings account and you save an
additional $5 per week. Your friend has $30 in his savings account and saves
an additional $10 per week. In how many weeks will you both have the same
amount of money in your accounts?
Lesson 6-2
Solve each system by using substitution.
6. x – y = 13
y – x = –13
7. 3x – y = 4
x + 5y = –4
8. x + y = 4
y = 7x + 4
Write and solve a system of equations by substitution.
9. A farmer grows corn and soybeans on her 300-acre farm. She wants to
plant 110 more acres of soybeans than corn. How many acres of each
crop does she need to plant?
10. The perimeter of a rectangle is 34 cm. The length is 1 cm longer than the
width. What are the dimensions of the rectangle?
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Name
Class
Date
Extra Practice (continued)
Chapter 6
Lesson 6-3
Solve each system by elimination.
11. x + y = 19
12. –3x + 4y = 29
x – y = –7
3x + 2y = –17
14. 6x + y = 13
y – x = –8
15. 4x – 9y = 61
13. 3x + y = 3
–3x + 2y = –30
16. 4x – y = 105
10x + 3y = 25
x + 7y = –10
Write and solve a system of equations using elimination.
17. Two groups of people order food at a restaurant. One group orders
4 hamburgers and 7 chicken sandwiches for $34.50. The other group orders
8 hamburgers and 3 chicken sandwiches for $30.50. Find the cost of each
item.
18. The sum of two numbers is 25. Their difference is 9. What are the two numbers?
Lesson 6-4
Write a system of equations to model each problem and solve.
19. A shoe store costs $1800 dollars a month to operate. The average wholesale
cost of each pair of shoes is $25, and the average price of each pair of shoes
is $65. How many pairs of shoes must the store sell each month to break
even?
20. Suppose you have 12 coins that total 32 cents. Some of the coins
are nickels and the rest are pennies. How many of each coin do
you have?
21. Claire bought three bars of soap and five sponges for $2.31. Steve
bought five bars of soap and three sponges for $3.05. Find the cost
of each item.
22. The perimeter of a rectangular lot is 74 feet. The cost of fencing along the
two lengths is $1 per foot, and the cost of fencing along the two widths is
$3.50 per foot. Find the dimensions of the lot if the total cost of the fencing
is $159.
23. A chemist wants to make a 10% solution of fertilizer. How much
water and how much of a 30% solution should the chemist mix to
get 30 L of a 10% solution?
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22
Name
Class
Date
Extra Practice (continued)
Chapter 6
24. Fruit drink A consists of 6% pure fruit juice and drink B consists of
15% pure fruit juice. How much of each kind of drink should you
mix together to get 4 L of a 10% concentration of fruit juice?
Write and solve a system of equations for each situation by any method.
Explain why you chose the method.
25. The ratio of boys to girls at a college is 4 : 5. How many boys and
girls are there if the total number of students is 3321?
26. A boat travels 18 miles downstream in 1.5 hours. It then takes the
boat 3 hours to travel upstream the same distance. Find the speed
of the boat in still water and the speed of the current.
Lesson 6-5
Determine whether the ordered pair is a solution of the linear inequality.
27. y > x – 7; (2, 5)
28. x ≤ 3; (–2, 6)
29. y ≥ 4x + 3; (3, 9)
30. y < x
31. y < x – 4
32. y > –6x + 5
33. y ≤ 14 – x
34.
35. 2x + 3y ≤ 6
Graph each linear inequality.
Write and graph a linear inequality for each situation.
36. Suppose you can spend up to $10 on bananas and apples.
Apples cost $3 per pound and bananas cost $1 per pound. List
three possible combinations of apples and bananas you can
buy.
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23
Name
Class
Date
Extra Practice (continued)
Chapter 6
37. Trenton is going to make a rectangular garden in his
yard. He wants the perimeter to be no larger than 40 ft.
What are three possible sets of dimensions that the
garden can have?
Lesson 6-6
Solve each system by graphing.
38. y ≤ 5x + 1
39. y > 4x + 3
y>x–3
y ≥ –2x – 1
41. y < –2x + 1
y > –2x – 3
40. y > –x + 2
42. y ≤ 5
y>x–4
43. y ≤ 5x – 2
y ≥ – x +1
44. Hideo plans to spend no more than $60 at an
entertainment store on DVDs and CDs. DVDs cost
$17 each and CDs cost $14 each. He wants to buy at
least two items. Write and graph a system of linear
inequalities that describes the situation. What are three
possible combinations of CDs and DVDs that he can
buy? Write and graph a system of inequalities that
describes the situation.
Prentice Hall Algebra 1 • Extra Practice
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24
y>3