PAGE 168 (Ch 6_Linear Inequalities)

Chapter 6 Linear Inequalities in Two Variables

From the table, it is found that only points from region B satisfy both the inequalities that are tested.
Thus, region B satisfies the inequalities x + y р 8 and y у 3.

9 y
8 x + y = 7 y = 43x + 2
Based on the diagram, determine the region that satisfies the

inequalities y р 3 x + 2 and x + y у 7.
4
6C
Solution:
4B
3 True/ True/ D
Region Point y 4 x+2 False x+yу7 False
A (4, 2) р True 4+2у7 False 2A
B (1, 5) 1+5у7
C (4, 7) 2 р 3 (4) + 2 False 4+7у7 False O 2468 x
D (8, 6) 4 8+6у7
False True
5 р 3 (1) + 2
4 True True

7 р 3 (4) + 2
4

6 р 3 (8) + 2
4

Region D satisfies both the inequalities y р 3 x + 2 and x + y у 7.
4

CHAPTER 6 6.2b y

1. Based on the diagram, determine the region that satisfies 8A y = 2x
each of the following systems of linear inequalities. 6 B
(a) y у 2x and y р 6. 4D
(b) y у 2x and y у 6. y=6
(c) y р 2x and y р 6. 2 C
(d) y р 2x and y у 6.
x
O 2468

2. Based on the diagram, determine the region that satisfies y
each of the following systems of linear inequalities.
(a) y р 6, y р x and x + y у 6. 8 x+y=6 y=x
6D F
(b) y р 6, y у x and x + y у 6. 4C y=6
2 BA
(c) y р 6, y р x and x + y р 6. E
O 24
(d) y у 6, y у x and x + y у 6. x
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