1. Linear Inequalities by Graphing
6.6 – Solving Systems of
Linear Inequalities by Graphing
Definitions of the Day (DODs)
System of Linear Inequalities
Solution to a System
of Linear Inequalites

2. Definition: System of Inequalities –
Two or more inequalities solved together. (by graphing)
Definition:
Solution to a System of Inequalities – Any region that is common to all inequalities
(makes all inequalities true)

3. Let’s Explore!! Test Points (0, 0) (0, 5) (3, 3) (1, 0) F F F T T T
T F

4. Let’s Explore!!
Test Points
(-3, 0)
(0, 0)
(5, 0)
T F
T T
F T

5. Solving Systems of Linear Inequalities by Graphing
Steps:
Carefully graph each inequality as if they
were equations.
2. Carefully test a point in each region for all inequalities.
Three possibilities:
- 4 regions if lines intersect at a point
- 3 regions if lines are parallel
- 2 regions if the same line
3. Shade the region where all of the inequalities are true.

6. Example

7. Example

8. Your Turn!!
Solve the following systems by graphing

9. Sentence Frames
In a system of inequalities, you shade the region where ___________________________________________
___________________________________________
There are three possibilities for the number of regions formed, They are: 1)__________________________________________
2)__________________________________________
3)__________________________________________