Section 5 Linear Inequalities in Two Variables

1
Chapter 7

• Section 5 Linear Inequalities in Two Variables

2
Graphing Inequalities Chapter 2.6

• x gt 4

open dot
1
2
3
4
5
6
7
8
9
3
Graphing Inequalities Chapter 2.6

• x 11

closed dot
5
6
7
8
9
10
11
12
13
4
Graphing Linear Inequalities
Any pt. in the shaded region is a solution to

• Graph

(-2, 5) ?
boundary line
True Statement
5
Graphing Linear Inequalities

• Graph

boundary line
(10, -6) ?
True Statement
6
Practice Graph the Inequality
Graph
Establish the boundary line.
?
?
x-intercept (let y 0)
y-intercept (let x 0)
7
Practice Graph the Inequality
Graph
? (3, 3)
Use a test point to determine the shading.
True. Therefore shade the right side of the
boundary.
8
Linear Inequalities in One Variable

• Graph y lt - 4 on a plane.

Establish the boundary line.
y - 4
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Linear Inequalities in One Variable

• Graph x lt 3 on a plane.

Establish the boundary line.
x 3
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Practice

• MathXL Ch 7 Section 5

11
Chapter 7

• Section 6 Systems of Linear Inequalities

12
Introduction

• Systems of equations can be solved by graphing.

(2,5)
?
x y 7 y 3x - 1
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Introduction
?

• Systems of inequalities can be also solved by
  graphing.

(1,2)
?
Solution Set
x y lt 7 x - y lt 4
?
?
?
x y lt 7
x - y lt 4
1 2 lt 7
1 - 2 lt 4
3 lt 7
-1 lt 4
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Example 1 of 3

• Graph the solutions to this system

Solution Set
x gt 3 x - 3y lt 6
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Example 2 of 3

• Graph the solutions to this system

Solution Set
x 2y lt 0 -2x x gt 2
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Example 3 of 3

• Graph the solutions to this system

x y lt 5 x gt 0 y gt 0 y lt 3
Solution Set
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Example 3 of 3

• Graph the solutions to this system

x y lt 5 x gt 0 y gt 0 y lt 3
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Example 3 of 3

• Graph the solutions to this system

x y lt 5 x gt 0 y gt 0 y lt 3
19
Practice

• MathXL Ch 7 Section 6 Homework