May 25th

May 25th

Graphing Systems of Inequalities

You can solve systems of inequalities by graphing. Recall that the graph of an inequality is a half-plane . The intersection of the two half-planes graphed in a system of inequalities represents the solution to the system.

Example

Graph the system of inequalities to find the solution.

x + y 3 and y + 3 x.

Solution

Begin by solving each inequality for y. Then, graph each inequality.

y -x + 3 and y x - 3

The solution to the system includes the ordered pairs in the intersection of the graphs of each inequality. This region is shaded dark gray. Notice that the boundary lines y = -x + 3 and y = x - 3 are included in the solution, since the inequalities contained and symbols.