Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 8 - Coordinate Geometry and Linear Systems - 8.7 - Graphing Linear Inequalities - Problem Set 8.7: 35

Answer

To graph an inequality, we first pretend that the inequality sign is an equal sign, and then we graph the equation. If it is a less than or equal to sign or a greater than or equal to sign, we make the line solid. If not, we make the line dashed. Next, we must shade the region. In order to do this, we pick any point not on the line. If that point satisfies the inequality, we shade the region to the side of the line that the point is in. If the point does not satisfy the inequality, we shade the region on the other side of the line. Once we graph one inequality, we can graph the other inequalities doing the same thing. The overlap of all inequalities is the solution to the system of inequalities.

Work Step by Step

As you can see on the attached graph, the overlap is once again a triangle whose base is on the x-axis from 0 to 2 and whose altitude is on the y-axis from 0 to 4.
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