Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 9 - Section 9.3 - Systems of Linear Inequalities - Exercise Set - Page 654: 18

Answer

Please see the graph.

Work Step by Step

Blue line: $2x+3y\le-8$ Orange line: $4x-y\ge-2$ Purple line: $y\ge-5$ To determine what sides of the lines to shade, we use a point not on the line. We can use (0,0) for the lines. Blue line: $2x+3y\le-8$ $2*0+3*0\le-8$ $0+0 \le -8$ $0\le-8$ (false, so we shade under the line) Orange line: $4x-y\ge-2$ $4*0-0\ge-2$ $0-0\ge-2$ $0\ge-2$ (true, so we shade the right side of the line) Purple line: $y\ge-5$ $0\ge-5$ (true, so we shade above the line) The solution area is the overlap of the three inequalities. In this case, the area is the triangle created at the three intersection points of $(−1,-2)$, $(1.75, -5)$, and $(3.5, -5)$.
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