Solving Systems of Inequalities by Graphing – Practice Problems

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Similar to systems of equations, systems of inequalities are two or more inequalities with the same two variables. To determine the solution to the system, or the point where the inequalities intersect (overlap), a graph is the best method to solve these problems.

First manipulate the inequalities in the system so they are written in slope-intercept form, y = mx + b. This makes it easier for you to create the graph. For each inequality in the system: First put a point on the y-intercept - indicated by the b-value. Next, use the m-value to draw in the slope. To connect the dots, you will use a dotted line to indicate less than or greater than, and a solid line is used for less than and equal to or greater than and equal to situations. Shade the area of the solution set.

This can be tricky – to avoid confusion, it’s a good idea to select a test point. Pop the coordinates of the test point into the inequality. If the inequality is true, shade the area indicated and if false, shade the other side of the line. Follow these steps for each inequality in the system, and the intersection of the shaded areas is the solution that makes all inequalities in the system true.

Solve systems of equations to find solutions to problems.

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Exercises in this Practice Problem
Explain how to solve a system of linear inequalities by graphing.
Find all solutions to Adventure Mike's riddle.
Determine where the party will take place.
Decide if the location of the treasure lies inside the area where the robbers are searching.
Describe how to determine the solution set for the inequality.
Assign the inequality.