6-8 Technology: Graph Systems of Inequalities
Name
Date
You can use a handheld to graph the system. ¨« y ⬎ 0 . 5 x ⫺ 2
©
«ª y ⱕ ⫺ 3 x ⫹ 5
Step 1 Press
. Then choose
to select Graphs & Geometry.
key to delete the equal sign.
Step 2 Use the
Input ⬎ 0.5x ⫺ 2.
Press
to graph the inequality.
Step 3 Use the
key to delete the equal
sign. Input ⱕ ⫺3x ⫹ 5. Use
to enter this inequality symbol.
Remember: The dashed line is not part of
the solution set.
Remember: The solid line is part of the
solution set.
Name two points that are part of the solution set.
Points (0, 1) and (⫺2, 0) appear to be part of the solution set.
Choose test points and check the solution algebraically.
Copyright © by William H. Sadlier, Inc. All rights reserved.
Use a handheld to graph the system. Then name two points that are
part of the solution set. Check students’ graphs and answers. Answers will vary.
1. ¨« y ⬍ 1
©
ª« y ⬎ 2 x ⫹ 2
2. ¨« y ⱕ ⫺x ⫹ 2
©
ª« y ⱕ 2
3. ¨« y ⬎ ⫺x
©
ª« y ⱕ 3
4. ¨« y ⱕ ⫺x ⫹ 1
©
ª« y ⱕ x ⫹ 1
5. ¨« y ⬎ 2 x ⫹ 1
©
ª« y ⬍ ⫺ 3 x ⫹ 4
6. ¨« y ⬎ 3 x ⫺ 1
©
ª« y ⬍ ⫺ 2 x ⫹ 4
7. ¨« y ⱕ x ⫹ 2
©
ª« y ⱕ ⫺x
8. ¨« y ⱕ x
©
ª« y ⱕ ⫺x ⫺ 3
9. ¨« y ⱖ ⫺ 5 x ⫹ 4
©
ª« y ⱖ 2 x ⫹ 3
10. ¨« y ⱖ ⫺ 4 x ⫹ 3
©
ª« y ⱖ 3 x ⫹ 7
11. ¨« y ⱖ ⫺ 13 x ⫺ 6
©
«ª y ⬍ 45 x ⫹ 9
Lesson 6-8, pages 168–169.
12. ¨« y ⱖ ⫺ 13 x ⫺ 2
©
«ª y ⬍ 43 x ⫹ 11
Chapter 6
157
For More Practice Go To:
Use a handheld to graph the system. Then name two points that are
part of the solution set. (Hint: Solve for y first.) Check students’ graphs and answers.
13. «¨2 x ⫹ y ⬎ 10
©
«ª x ⫺ 2 y ⬍ 8
14. «¨3 x ⫹ y ⬎ 8
©
«ª x ⫺ 3 y ⬍ 9
15. «¨ x ⫹ 4 y ⱖ 3
©
«ª x ⫺ 5 y ⬎ 12
16. «¨ x ⫹ 2 y ⱖ 7
©
«ª x ⫺ 6 y ⬎ 11
17. «¨5 x ⫹ 4 y ⬍ ⫺ 24
©
«ª3 x ⫺ 7 y ⬎ 52
18. «¨6 x ⫹ 5 y ⬍ ⫺ 32
©
«ª4 x ⫺ 9 y ⬎ 64
19. «¨4 x ⫹ 10 y ⱕ 58
©
«ª3 x ⫹ 8 y ⱕ 29
20. «¨5 x ⫹ 2 y ⱕ 27
©
«ª4 x ⫹ 3 y ⱕ ⫺ 18
21. «¨2 . 1 x ⫹ 3 . 4 y ⬎ 1 . 5
22. ¨«3 . 8 x ⫹ 1 . 7 y ⬎ 7 . 2 23. ¨«4 . 5 x ⫺ 6 . 8 y ⬍ ⫺ 12 . 3 24.
©
©
©
«ª1 . 7 x ⫹ 5 . 6 y ⬎ ⫺ 9 . 8
«ª5 . 2 x ⫹ 4 . 8 y ⬎ ⫺ 2 . 3
«ª8 . 01 x ⫹ 2 . 2 y ⬎ 4 . 9
«¨2 . 1 x ⫺ 4 . 3 y ⬍ ⫺ 11 . 5
©
«ª7 . 9 x ⫹ 4 . 51 y ⬎ 7 . 3
Solve.
25. Graph the system on a handheld. Then describe the solution set.
Explain your reasoning.
Check that students graph a rectangle. Rectangle; perpendicular intersecting lines form four right angles.
26. The school band is selling 280 shirts and 150 shorts stamped with the
school logo. They need sales of at least $2000. A shirt sells for $19.95
and shorts sell for $12.95. How many of each do they need to sell to have
at least $2000? (Hint: Use
: Choose Window and A: Zoom — Fit.)
19.95x ⴙ 12.95y ⱖ 2000
. Students should consider only x # 280.
y ⱕ 150
Answers will vary. Possible answer: 5 shirts and 150 shorts or 50 shirts and 78 shorts
Graph the system
{
27. Graph a system of inequalities that has no solution. Explain how
you created the system.
Check that students graph parallel lines or one dashed line with shading above and below.
Explanations should include that the shaded regions do not overlap.
158
Chapter 6
Copyright © by William H. Sadlier, Inc. All rights reserved.
¨y ⬎ ⫺ 3 x ⫺ 5
4
«
4
«« y ⬎ x ⫹ 8
3
©
«3 x ⫹ 4 y ⱕ 4
«
«ª4 x ⫺ 3 y ⱕ 9