Objectives
To solve systems of linear inequalities by graphing
To model real-world situations using systems of linear inequalities
A system of linear inequalities is made up of two or more linear inequalities. A solution of a system of linear inequalities is an ordered pair that makes all the inequalities in the system true. The graph of a system of linear inequalities is the set of points that represent all of the solutions of the system.
Essential Understanding You can graph the solutions of a system of linear inequalities in the coordinate plane. The graph of the system is the region where the graphs of the individual inequalities overlap.
What is the graph of the system?
Have you seen a problem like this before?
Yes. The solution of a system of equations is shown by the intersection of two lines. The solutions of a system of inequalities are shown by the intersection of two shaded areas.
Graph
The system's solutions lie in the green region where the graphs overlap.