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.
Graph the system of inequalities to find the solution.
x + y 3 and y + 3 x.
Begin by solving each inequality for y. Then, graph each
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.