﻿ GreeneMath.com - Solving Systems of Linear Inequalities Lesson

# In this Section:

In this section, we learn how to graph a system of linear inequalities in two variables. We begin by graphing each inequality separately. To perform this action quickly, we solve each inequality for y. We then replace the inequality symbol with an equality symbol. Graphing this equality, gives us the boundary line. This line will separate the solution region from the non-solution region. The boundary line is dashed for a strict inequality (boundary line is not part of the solution region). When the inequality is non-strict, our boundary line is solid (boundary line is part of the solution region). Once we have drawn our boundary line, we proceed to shade above the boundary line for a greater than or below the line for a less than. Once each inequality is graphed, we look for the intersection or overlap of the solution regions. This area will satisfy both inequalities and will be our solution for the system.
Sections:

# In this Section:

In this section, we learn how to graph a system of linear inequalities in two variables. We begin by graphing each inequality separately. To perform this action quickly, we solve each inequality for y. We then replace the inequality symbol with an equality symbol. Graphing this equality, gives us the boundary line. This line will separate the solution region from the non-solution region. The boundary line is dashed for a strict inequality (boundary line is not part of the solution region). When the inequality is non-strict, our boundary line is solid (boundary line is part of the solution region). Once we have drawn our boundary line, we proceed to shade above the boundary line for a greater than or below the line for a less than. Once each inequality is graphed, we look for the intersection or overlap of the solution regions. This area will satisfy both inequalities and will be our solution for the system.