College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 5 - Systems of Equations and Inequalities - Exercise Set 5.5 - Page 572: 47

Answer

The solution set is the region shaded GRAY
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Work Step by Step

We will graph the solution region for each inequality. 1. (red) $x^{2}+y^{2}=4^{2}$ is a circle centered at the origin, radius = 4. Border: solid line ( sign is $\leq )$, Testing $(0,0):\quad 0 + 0^{2} \leq 16\quad?$ Yes, shade the region containing $(0,0)$ 2 (blue) To graph a line, we need two points...unless we know it is vertical or horizontal. $x+y=2 \quad $dashed line ( sign is $> )$, x-intercept:$\quad x+0=2\quad$ point: ($2,0)$ y-intercept:$ \quad 0+y=2\quad$ point: ($0,2)$ Testing $(0,0)$:$\quad 0+0 \geq 2 \quad ?$ No, shade the region not containing (0,0) The solution set is the region with BOTH shadings. The solution set is the region shaded GRAY
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