Definitions of the Day (DODs)

6.6 – Solving Systems of Linear Inequalities by Graphing

• System of Linear Inequalities• Solution to a System of Linear Inequalites

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)

Let’s Explore!! Graph

3 1y x

Graph

3x y

Test Points(0, 0)(0, 5)(3, 3)(1, 0)

F FF TT TT F

Let’s Explore!! Graph

3 1y x

Graph

3 2y x Test Points

(-3, 0)(0, 0)(5, 0)

T FT TF T

Steps:1. 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.

Solving Systems of LinearInequalities by Graphing

Example3

22Graph:

12

2

y x

y x

Example4 4

Graph: 12

4

x y

y x

Your Turn!!

4

2

y

x

1. Solve the following systems by graphing

3 4

2 1

y x

y x

Sentence Frames

1. In a system of inequalities, you shade the region where ___________________________________________

___________________________________________

2. There are three possibilities for the number of regions formed, They are: 1)__________________________________________2)__________________________________________3)__________________________________________