Key Concepts

• To graph an inequality, first graph the related boundary line by replacing the given inequality symbol with the equality symbol to find its equation. Use a dashed line for a strict inequality. Then, test ordered pairs on either side of the boundary line and shade the side of the graph containing the point that satisfies the inequality equation.
• The solution to a system of linear inequalities is the region containing all the ordered pairs satisfying the system.
• You can verify whether a point is a solution to a system of linear inequalities in the same way you verify whether a point is a solution to a system of equations.
• Systems of inequalities have no solutions when boundary lines are parallel.
• Systems of inequalities can be used to model certain business situations.

Glossary

boundary line

replacing the inequality symbol of an inequality with an equality symbol and graphing the resulting line will yield the boundary line of the inequality

solution region

all possible points [latex](x, y)[/latex] on a graph that satisfy an inequality or system of inequalities

system of inequalities

two or more inequalities with the requirement that solutions for the system must be solutions of all inequalities in the system