Answers

Name
Class
Date
Practice
6-6
Form G
Systems of Linear Inequalities
Solve each system of inequalities by graphing.
2. 5x 2 y # 1
1. 3x 1 y # 1
3. 4x 1 3y # 1
x 1 3y # 22
x2y#3
2x 2 y # 2
y
y
y
4
4
4
2
2
2
x
x
O
Ź4 Ź2
2
4
O
Ź4 Ź2
2
x
4
O
Ź4 Ź2
Ź2
Ź2
Ź2
Ź4
Ź4
Ź4
2
4
4. Writing What is the difference between the solution of a system of linear
inequalities and the solution of a system of linear equations? Explain.
The graph of a system of linear equations is made up of lines, so the solution, if it
exists, is a single point. The graph of a system of linear inequalities is made up of
shaded half-planes, so if a solution exists, it is a region where the shaded regions
overlap.
5. Open-Ended When can you say that there is no solution for a system of
linear inequalities? Explain your answer and show with a system and graph.
Answers may vary. Sample: There is no solution to a system of inequalities when
the boundary lines are parallel and the shaded regions do not overlap. Example:
y K x 2 1; y L x 1 2; Check students’ graphs.
6. Error Analysis A student graphs the system below.
Describe and correct the student’s error.
y
8
x2y$3
4
x
y , 22
Ź8
x$1
O
Ź4
4
Ź4
When graphing the inequality x L 1, the student
shaded the wrong half of the plane.
Ź8
Determine whether the ordered pair is a solution of the given system.
7. (0, 1);
9. (1, 4);
8. (22, 3);
1 2 x $ 3y
3y 2 1 . 2x
2x 1 3y . 2
3x 1 5y . 1
2x 1 y . 3
23x 2 y # 5
not a solution
solution
solution
Prentice Hall Gold Algebra 1 • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
53
8
Name
Class
Date
Practice (continued)
6-6
Form G
Systems of Linear Inequalities
10. Mark is a student, and he can work for at most 20 hours a week.
Hours dog walking
He needs to earn at least $75 to cover his weekly expenses. His
dog-walking job pays $5 per hour and his job as a car wash
attendant pays $4 per hour. Write a system of inequalities to
model the situation, and graph the inequalities.
20
18
16
14
12
10
8
6
4
2
x 1 y K 20, 4x 1 5y L 75
y
x
O
12
6
18
24
30
Hours at car wash
She wants to make banana bread that sells for $1.25 each and
nut bread that sells for $1.50 each and make at least $24 in sales.
Write a system of inequalities for the given situation and graph
the inequalities.
x 1 y K 10, 1.25x 1 1.5y L 24
Nut Bread
11. Britney wants to bake at most 10 loaves of bread for a bake sale.
20
18
16
14
12
10
8
6
4
2
O
y
x
6
12
8
y S257x 2 67, y R213x 2 13
(24, 2)
(24, 1)
Ź8
14. x 1 4y 2 2 $ 0
13. 5x 1 7y . 26
y
4
4
2
2
O
4
x
Ź4 Ź2
O
Ź2
Ź2
Ź4
Ź4
2
4
x
15. 2 2 5 . 26y
3x 1 y . 2
y
4
2
x
Ź4 Ź2
O
2
4
Ź2
Ź4
Prentice Hall Gold Algebra 1 • Teaching Resources
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
54
y
(2, 21)
O
Ź8
x
30
4
Ź4
y
2
Ź4 Ź2
Ź4
2x 2 y 1 1 . 2
x 1 3y , 21
24
Banana Bread
12. Write a system of inequalities for the following graph.
Solve each system of inequalities by graphing.
18
4
(3, 23)
x
8

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