Key Idea: Systems of Inequalities

A system of inequalities consists of two or more inequalities with the same variables.
The solution is the set of points that satisfy all inequalities at once.

General Rule:

• Graph each inequality on a coordinate plane.

• The solution is the overlapping (shaded) region of all inequalities.

• Some systems may have no solution if regions don’t overlap.

Why this matters for the SAT:

Systems of inequalities appear in coordinate geometry and word problems.
Recognizing the overlapping region helps you quickly identify all solutions that satisfy the system.