Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 3 - Section 3.7 - Graphing Linear Inequalities - Exercise Set - Page 188: 69

Answer

Please see the graph.

Work Step by Step

Orange line: $x\ge0$ Green line: $y\ge0$ Blue line: $2x+4y\le40$ Since all three lines are either "less than or equal to" or "greater than or equal to", we will shade with solid lines. Let's use the point $(0,0)$ to determine what side of the lines to shade. Orange line: $x\ge0$ $x\ge0$ $0 \ge 0$ (true) This is true, so we shade the side of the line with the point $(0,0)$. Green line: $y\ge0$ $y\ge0$ $0\ge0$ (true) This is true, so we shade the side of the line with the point $(0,0)$. Blue line: $2x+4y\le40$ $2x+4y\le40$ $2*0+4*0\le40$ $0+0 \le 40$ $0 \le 40$ (true) This is true, so we shade the side of the line with the point $(0,0)$. We want the intersection of the three graphs, so where all three graphs are shaded is the intersection. The boundaries of the intersection are $(0,0)$, $(20,0)$, and $(0,10)$ (as shown on the graph).
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