Intermediate Algebra (6th Edition)

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

Chapter 4 - Section 4.5 - Systems of Linear Inequalities - Exercise Set - Page 243: 18

Answer

Please see the graph.

Work Step by Step

Green line: $4x-y\ge-2$ Blue line: $2x+3y\le-8$ Orange line: $y\ge-5$ Let's use the point $(0,0)$ to determine what sides of the lines to shade. Green line: $4x-y\ge-2$ $4x-y\ge-2$ $4*0-0\ge -2$ $0-0\ge -2$ $0 \ge -2$ (true) This is true, so we shade the side of the line that does have the point. The inequality has the "greater than or equal to" sign, so we use a solid line. Blue line: $2x+3y\le-8$ $2x+3y\le-8$ $2*0+3*0\le-8$ $0+0 \le -8$ $0 \le -8$ (false) This is false, so we shade the side of the line that doesn't have the point. The inequality has the "less than or equal to" sign, so we use a solid line. Orange line: $y\ge-5$ $y\ge-5$ $0 \ge -5$ (true) This is true, so we shade the side of the line that does have the point. The inequality has the "greater than or equal" sign, so we use a solid line. The solution area for the system on inequalities is the area that is shaded blue, green, and orange.
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