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: 16

Answer

Please see the graph.

Work Step by Step

Blue line: $5x+3y\ge-2$ Orange line: $y+2x\leq0$ Purple line: $y\leq4$ 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: $5x+3y\ge-2$ $5*0+3*0\ge-2$ $0\ge-2$ (true, so we shade the right side of the line) Orange line: $y+2x\leq0$ $0+2*0\leq0$ $0\leq0$ (true, so we shade the left side of the line) Purple line: $y\leq4$ $0\leq4$ (true, so we shade below 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 $(-2.8,4)$, $(-2,4)$, and $(2, -4)$.
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