## 6-6 Solving Systems of Linear Inequalities

**Objective**: Graph and solve systems of linear inequalities in two variables.

Solving a system of linear inequalities, just as solving a system of linear equations, is like solving two individual inequalities within one problem. The solutions to a system of linear inequalities will be the portion of the graph that is shaded by BOTH inequalities.

The graph on the right represents a system of linear inequalities. The shaded blue half-plane represents the solutions of the blue inequality while the shaded red/pink half-plane represents the solutions to the red inequality.
The part of the graph that is shaded by both the red AND the blue represents the solutions to BOTH inequalities, therefore, is the solution set for the system. |

Just as special system of linear equations, there are "special" systems of linear inequalities with the same slope (parallel lines) that will create some questions.