Graphing Systems of Inequalities

Once you've learned how to graph linear inequalities, you can move on to solving systems of linear inequalities. A "system" of linear inequalities is a set of linear inequalities that you deal with all at once. Usually you start off with two or three linear inequalities. The technique for solving these systems is fairly simple. Here's an example. Solve the following system: 2x – 3y < 12 x + 5y < 20 x > 0 Just as with solving single linear inequalities, it is usually best to solve as many of the inequalities as possible for "y" on one side. Solving the first two inequalities, I get the rearranged system: y > ( 2/3 )x – 4 y < ( – 1/5 )x + 4 x > 0

"Solving" systems of linear inequalities means "graphing each individual inequality, and then finding the overlaps of the various solutions". So I graph each inequality, and then find the overlapping portions of the solution regions.