Inequalities

Solving Systems of Inequalities

Solving Systems of Inequalities

Solving systems of inequalities with two variables is similar to solving systems of inequalities with one variable. First, graph each inequality, lightly shading their respective regions. The region that is shaded in the graphs of both inequalities--the intersection of the two--is the solution to the system of inequalities.

Example 1: Solve the following system of inequalities:

2x - y≤2
2y + x < 2

The darkest shaded region is the solution to the system--all the points in that region satisfy both inequalities.

PARGRAPH
Example 2: Solve the following system of inequalities:

y≥x ² - 2
x≥ - 3y + 6

Once again, the darkest shaded region is the solution to the system--all the points in that region satisfy both inequalities.