System of Linear Inequalities

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In this section, we learn about Systems of Linear Inequalities. We will explain how to graph the solution for a system of linear inequalities in two variables. We begin by revisiting our methods to graph the solution for a linear inequality in two variables. Recall that the quickest method to perform this operation involves us solving the inequality for y and graphing the boundary line. After the boundary line is drawn, we shade based on our inequality symbol. We shade above the line for a greater than or greater than or equal to, and we shade below the line for a less than or a less than or equal to. Once we have graphed each inequality, we are simply finding the intersection of the two solution regions. This will give us a section of our coordinate plane that satisfies both inequalities of the system.
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