Graphing Systems of Linear Inequalities

• It is assumed you already know how to graph a linear inequality, which was discussed in a previous module.

• Graphing a system of linear inequalities means to graph two or more inequalities.

• To solve a system of linear inequalities:

1) Graph each inequality in the system, shading each with a different pattern.

2) Determine the intersection of the graphs. It is the solution of the system.

• Example 1

3

3

x y

x y

Solve:

Graph the first inequality.

2

-2

-4

5

3x y

2

-2

-4

5

Graph the second inequality. 3x y

2

-2

-4

5

The solution to the system is the part where the two graphs overlap, including the lower part of the blue line.