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 187: 42

Answer

Please see the graph.

Work Step by Step

Green line: $x+y\le0$ Since we have the "less than or equal to" sign, we use a solid line. Let's use the point $(0,0)$ to see what side of the line we shade. $x+y\le0$ $x+y\le0$ $0 \le 0$ (true) Since this is true, we shade the side of the line that has the point $(0,0)$. Red line: $3x-6y\ge12$ $3x-6y\ge12$ $3x-6y+6y-12\ge12+6y-12$ $3x-12\ge6y$ $(3x-12)/6\ge6y/6$ $.5x-2 \ge y$ Since we have the "greater than or equal to" sign, we use a solid line. Let's use the point $(0,0)$ to see what side of the line we shade. $.5x-2 \ge y$ $.5*0-2 \ge 0$ $0-2 \ge 0$ $-2 \ge 0$ (false) Since this is false, we shade the side of the line that doesn't have the point $(0,0)$. The intersection of the two lines is the area that is shaded red and green.
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