Solution Set (Systems of Linear Inequalities)
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
The solution set for a system of linear inequalities is the set of all points (usually in the coordinate plane) that satisfy every inequality in the system simultaneously.
To find the solution set for a system of linear inequalities, you:
Graph each inequality: Each inequality represents a half-plane. You graph the boundary line (or curve) and shade the region that satisfies the inequality.
Find the intersection: The solution set is the region where all the shaded areas of the inequalities overlap. This is the area where all the inequalities hold true.
For example, in a system like:
y < 2x + 3
y > -x + 1
The solution set is the region where both inequalities are true. This is the overlapping area on the graph where points (x, y) satisfy both inequalities.
So, the solution set consists of all the points that lie in the intersection of the shaded regions on the graph.