Graph Solutions to Systems of Linear Inequalities

Learning Outcomes

  • Solve systems of linear inequalities by graphing the solution region
  • Graph solutions to a system that contains a compound inequality

We will continue to practice graphing the solution region for systems of linear inequalities. We will also graph the solutions to a system that includes a compound inequality.


Shade the region of the graph that represents solutions for both inequalities. [latex]x+y\geq1[/latex] and [latex]y–x\geq5[/latex].

The videos that follow show more examples of graphing the solution set of a system of linear inequalities.

The system in our last example includes a compound inequality.  We will see that you can treat a compound inequality like two lines when you are graphing them.


Find the solution to the system [latex] 3x + 2y < 12 [/latex] and [latex] -1 ≤ y ≤ 5 [/latex].

In the video that follows, we show how to solve another system of inequalities that contains a compound inequality.