# Solving Systems of Linear Inequalities Graphically

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A system of inequalities is a set of two or more inequalities analyzed together. In this course, linear systems in

**two**inequalities will be explored. This section discusses how to graph and solve these systems.## System of Inequalities

The following system of inequalities contains two conditions on the variables $x$ and $y.$ $\begin{cases}y \leq \text{-} 0.5x+3 \\ y > x \end{cases}$ Systems of inequalities are often illustrated graphically in a coordinate plane, where the inequalities define a region.

## Graphing a System of Linear Inequalities

Individual inequalities can be interpreted graphically as the area above or below a boundary line. When all inequalitites in a system are graphed, the solution to the system is the overlapping region of the individual solution sets.
For example, the following system can be solved in this way.
$\begin{cases}x+y<7 \\ x+2y<10 \end{cases}$

## Exercises

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