Graphing Systems of Linear Inequalities

Graphing Systems of Linear Inequalities

Example: Graph the system:

Solution:

To graph the inequality $x + y\leq 4$ we graph $x + y = 4$ using a solid line. We then consider (0,0) as a test point and find that it is a solution, we shade all points in that region.

Next, we graph $x - y < 4$. We graph $x - y = 4$ as a dashed line and consider (0,0) as a test point. Again (0,0) is a solution, we shade that region. Finally, the solution set of the system is the region that is commonly shaded in both inequalities.

This dark shaded region is a solution of these inequalities.

Example: Graph the system of inequalities.