Systems of Equations and Inequalities: System of Linear Inequalities

Now that we know what a solution to a system of inequalities looks like, let’s go through how to graph and find the solution from beginning to end.

The process involves graphing the separate inequalities and identifying where the shading overlaps. Let’s look at an example.

Find the solution of:

2x + y < 2
x ≥ -4

First, let's graph x ≥ -4.

Graph of x is greater than or equal to negative four

Next, graph 2x + y < 2 on top of your existing graph.

Graph of x is greater than or equal to negative four and two x plus y is less than two

Finally, only graph the portion of the graph where the shading overlaps. This is the solution to the system of linear inequalities.

Solution to of x is greater than or equal to negative four and two x plus y is less than two