Math - System of Inequalities

A system of inequalities is a set of two or more inequalities considered together. The solution is the set of values that satisfy all the inequalities at once.

One Variable Inequality

A one-variable inequality represents a horizontal or vertical line (y, x) on a graph, with one side shaded.

Two Variables Inequality

A two-variables inequality represents straight line on a graph, with one side shaded.

Solving a System of Inequalities

To solve a system of inequalities:

1. Graph each inequality on the same coordinate plane.
2. Shade the solution region for each inequality.
3. Identify the overlapping region.

Examples

Consider the system of inequalities:

• 2x + 4y $\ge$ 12
• 2x - 3y > 2

Consider the system of inequalities:

• x < 3
• y > -4
• y $\le$ 2x + 4

Consider the system of inequalities:

• x $\ge$ 5
• y > 4
• x + y < 10