# Question about Systems of Linear Inequalities

How many solution sets do systems of linear inequalities have? Must solutions to systems of linear inequalities satisfy both inequalities? In what case might they not? Use an example for discussion.

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#### Solution Preview

Systems of linear inequalities could have multiple solutions or no solutions at all. Looking at several examples;

y<x and y<-x

In this case, the graph of the linear function of the inequality is simply y=x and y=-x. Because of the "and" condition, solutions of the system must be true for both linear inequality equations. When we graph this solution, we see that the solution consists of the region formed below BOTH lines, which we would shade ...

#### Solution Summary

Solution sets of systems of linear equalities may or may not exist. This solution discusses both cases with examples.