Systems of Linear Inequalities

A system of inequalities is two or more inequalities that must be satisfied simultaneously. The solution is the overlap region — the area on the graph where ALL shaded regions intersect. [formula] Each inequality defines a half-plane. The solution set is where both half-planes overlap.

1. Graph each inequality separately (with correct shading and dashed/solid lines) 2. Find the overlap region — this is the solution 3. Any point in the overlap satisfies all inequalities With Desmos: type both inequalities. Desmos shows the overlap as the darkest shaded region. This is by far the fastest method on the SAT.

Example: Find a point in the solution set of: [formula]