$Inequalities on a Plane$

Inequalities on a Plane

The solution of a system of linear inequalities in x and y on the plane, with the vertices of the region.

For example: x + y <= 6, 2x − y > 1, y >= 0. A strict inequality is drawn with a dashed boundary.

This calculator draws the solution of a system of linear inequalities in x and y on the coordinate plane and finds the vertices of the region.

Replace the inequality sign with an equals sign and draw the line. For a strict inequality the line is dashed.
Substitute a test point that is not on the line, such as (0, 0). If the inequality holds, the half-plane containing this point fits.
The solution of the system is the part common to all half-planes.

Example. The system x + y ≤ 6, x ≥ 0, y ≥ 0 defines a triangle with vertices (0, 0), (6, 0) and (0, 6).