1. Section
9.4
Graphing Linear Inequalities in Two Variables and Systems of Linear Inequalities

2. Graph a Linear Inequality in Two Variables.
Objective 1
Graph a Linear Inequality in Two Variables.

3. Linear Inequalities in Two Variables
Linear inequality in two variables
Can be written in one of the forms
Ax + By < C Ax + By  C
Ax + By > C Ax + By  C
A, B, and C are real numbers, A and B are not both 0.
An ordered pair is a solution of the linear inequality if it makes the inequality a true statement. 3

4. Linear Inequalities in Two Variables
To Graph a Linear Inequality in Two Variables
1. Graph the boundary line found by replacing the inequality sign with an equal sign.
If the inequality sign is > or <, graph a dashed boundary line (indicating that the points on the line are not solutions of the inequality).
If the inequality sign is  or , graph a solid boundary line (indicating that the points on the line are solutions of the inequality).
2. To shade  or > = up and  or < = down.
OR Choose a point, not on the boundary line, as a test point. Substitute into the original inequality. True = shade half-plane that contains that point, and false = shade half-plane that does not contain that point. 4

5. Example
Graph 7x + y > –14
(0,0)

6. Example
Graph 3x + 5y  –2.

7. Example
Graph 3x < 15.

8. Linear Inequalities in Two Variables
Warning!
Note that although all of our examples allowed us to select (0, 0) as our test point, that will not always be true.
If the boundary line contains (0,0), you must select another point that is not contained on the line as your test point. 8

9. We will complete 9.4 Tomorrow
Practice Worksheet – turn in before you leave Homework: p. 585 #1-5 odds and odds

10. Solving a System of Linear Inequalities
Objective 1
Solving a System of Linear Inequalities

11. Systems of Linear Inequalities
Two linear inequalities make a system of linear inequalities.
A solution of a system of linear inequalities is an ordered pair that satisfies each inequality in the system.
Graphing the Solution of a System of Linear Inequalities
Step 1: Graph each inequality in the system on the same set of axes.
Step 2: The solutions (or solution region) of the system are the points common to the graphs of all the inequalities in the system. 11

12. Example
Graph the solution of the system:

13. Example 3x + y < 9 Graph the solution of the system: 2x + 5y  10
The solution will be the set of all points that satisfy both of the inequalities in the system. y x 4
The boundary line is 3x + y = 9.
Solution
The boundary line is
2x + 5y = 10

14. Example y > 2x + 4 Graph the solution of the system: y < 2x – 21 2 3 4 1 2 3 4
y > 2x + 4
This system has no solution.
y < 2x – 2

15. Example
Graph the solution of the system:

16. Done with Lesson 9.4 Practice Worksheet – turn in before you leave
Homework: p. 585 #55-67 odds