Name ——————————————————————— Date ————————————

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Practice AFor use with the lesson “Solve Systems of Linear Inequalities”

Tell whether the ordered pair is a solution of the system of inequalities.

1. (2, 1) 2. (23, 2) 3. (0, 21)

x

y

1 3 521

3

x

y

121

212325

1

3

x

y

1 32123

1

4. (22, 0) 5. (2, 4) 6. (22, 3)

x

y

12325

3

23

x

y

1 3

3

1

21

x

y

3121

23

21

1

3

Match the system of inequalities with its graph.

7. x 1 y ≥ 4 8. x 1 y ≤ 4 9. x 2 y ≥ 4

x < 2 x < 22 y > 2

10. y 1 x ≤ 4 11. x 2 y ≤ 4 12. y 1 x ≥ 4

y < 2 x > 22 y < 22

A.

x

y

6 10222

22

6 B.

x

y

6226

6

10

2

C.

x

y

6226 22

6

26

22

D.

x

y

626 22

6

2

22

E.

x

y

6 102

26

22

6

2

F.

x

y

6226

2

22

Les

so

n 6

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Algebra 1Chapter Resource Book6-68

Lesson

6.6

CS10_CC_A1_MECR710723_C06L06PA.indd 68 5/13/11 11:17:51 PM

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Practice A continuedFor use with the lesson “Solve Systems of Linear Inequalities”

Graph the system of inequalities.

13. x > 21 14. y > 23 15. x ≥ 2

x < 4 y ≤ 0 y > 0

x

y

1

3

1212321

23

3

x

y

1

3

1212321

23

3

x

y

1

3

1212321

23

3

16. x < 1 17. x > 0 18. y ≤ 3

y ≤ 22 y ≤ x y > 2x

x

y

1

3

1212321

23

3

x

y

1

3

1212321

23

3

x

y

1

3

1212321

23

3

19. Ordering Cups You work at an Italian ice shop during

x00123456789

1 2 3 4 5 6 7 8 9Boxes of 5-ounce cups

Bo

xes

of

8-o

un

ce c

up

s

y

the summer. You need to order 5-ounce and 8-ounce cups. The storage room will only hold 10 more boxes of cups. A box of 5-ounce cups costs $15 and a box of 8-ounce cups costs $18. A maximum of $90 is budgeted for cups.

a. Let x represent the number of boxes of 5-ounce cups and let y represent the number of boxes of 8-ounce cups. Write a system of linear inequalities for the number of cups that can be bought.

b. Graph the system of inequalities.

c. Identify two possible combinations of cups you can buy.

20. Studying You need at least 4 hours to do your science and

x00123456

1 2 3 4 5 6Hours spent on science

Ho

urs

sp

ent

on

his

tory y

history homework. It is 1:00 p.m. on Sunday and your friend wants you to go to the movies at 7:00 p.m.

a. How much time do you have between now and 7:00 p.m. to do your homework?

b. Let x represent the number of hours spent on science homework and let y represent the number of hours spent on history homework. Write and graph a system of linear inequalities that shows the number of hours you can work on each subject if you go to the movies.

Less

on

6.6

Algebra 1Chapter Resource Book 6-69

Lesson

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CS10_CC_A1_MECR710723_C06L06PA.indd 69 5/13/11 11:17:52 PM

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an

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s

Lesson Solve S pecial Types of Linear Systems, continued

Study Guide

1. infinitely many solutions 2. no solution

3. infinitely many solutions 4. one solution

5. one solution

Real-Life Application

1.

x

y

4

42424

212

212 12 20

Yes, there is a possibility because the two lines intersect.

2. The two equations represent the same line. If the cubs are walking towards you, then yes, you will see them. If the cubs are walking away from you, then no, you will not see them. 3. No, you will not cross the stream. The two lines are parallel.

Challenge Practice

1. a 5 1 } 2 2. No value of a gives infinitely many

solutions. 3. a Þ 1 }

2 4. The number of solutions

depends only on the value of c. 5. When c 5 4 there are an infinite number of solutions. When c Þ 4 there are no solutions.

6. x 5 c1b2 2 c2b1

} a1b2 2 a2b1

; y 5 a1c2 2 a2c1

} a1b2 2 a2b1

7. a1b2 Þ a2b1 8. a1b2 5 a2b1 and c2 Þ b2

} b1 c1

9. a1b2 5 a2b1 and c2 5 b2

} b1 c1

Lesson Solve Systems of Linear Inequalities

Teaching Guide

1.

23 1 3

1

23

3

x

y

(22, 3)

2. y ≥ 2x 1 1 3. y ≤ 2x 1 2

4. The shaded region is the intersection of the regions that are the solutions of the two inequalities.

Spreadsheet Activity

1. not a solution; not a solution; solution; not a solution 2. solution; not a solution; not a solution; solution

Practice Level A

1. yes 2. no 3. yes 4. no 5. yes 6. yes

7. D 8. B 9. A 10. C 11. F 12. E

13.

x

y

1

3

123 3

14.

x

y

1

3

1212321

3

15.

x

y

1

3

1212321

23

3

16.

x

y

1

3

1212321

23

3

17.

x

y

1

3

12123

23

3

18.

x

y

1

1212321

23

3

19. a. x 1 y ≤ 10 and 15x 1 18y ≤ 90 b.

x00123456789

1 2 3 4 5 6 7 8 9Boxes of 5-ounce cups

Bo

xes

of

8-o

un

ce c

up

s

y c. Answers will vary.

20. a. 6 h b.

x00123456

1 2 3 4 5 6Hours spent on science

Ho

urs

sp

ent

on

his

tory

x 1 y < 6

x 1 y > 4

y

c. Answers will vary.

Algebra 1Chapter Resource Book A77

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