# Solving Systems of Inequalities

## Overview

### Description

When solving systems of inequalities, graph the inequalities in the system, and find where the solutions overlap. This concept can be used to find the best possible combination of the variables in order to maximize or minimize a function under certain conditions. Systems of inequalities may include linear or nonlinear relationships. Like systems of equations, some systems of inequalities have no solutions.

### At A Glance

• The solutions of an inequality in two variables are represented on a graph by shading the region above or below the graph of the related equation.
• The solution of a system of linear inequalities is represented on a graph as the overlap of the shaded regions that represent the solutions of the separate inequalities.
• Linear programming is used to find the maximum or minimum value of a function that is subject to a set of constraints.
• The solution of a system of nonlinear inequalities is represented on a graph as the overlap of the shaded regions that represent the solutions of the separate inequalities.