Graphing Inequalities & Systems

A linear inequality in two variables, like $y \le x + 3$, is solved not by a single line but by a whole half-plane — every point on one side of the boundary line. A system of inequalities asks for the points that satisfy all of them at once: the overlap of the half-planes.

• The boundary is solid when the inequality includes equality ($\le$ or $\ge$) and dashed when it is strict ($<$ or $>$).
• To check a point, substitute it into every inequality — it is a solution only if it makes them all true.
• The solution of a system is the region where the shadings overlap; a point in that region works in every inequality.

These are real, released Regents questions.