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: 52

Answer

The solution set is the region shaded GRAY .

Work Step by Step

We will graph the solution region for each inequality. 1. (red) $(x+1)^{2}+(y-1)^{2}=4^{2}$ is a circle centered at $(-1,1)$, radius = $4$. Border: dashed line ( sign is $< )$, Testing $(-1,1):\quad (-1)^{2} + 1^{2} < 16\quad?$ Yes, shade the region containing $(1,-1).$ 1. (blue) $(x+1)^{2}+(y-1)^{2}=2^{2}$ is a circle centered at $(-1,1)$, radius = $2$. Border: solid line ( sign is $\geq )$, Testing $(-1,1):\quad (-1)^{2} + 1^{2} \geq 4\quad?$ No, shade the region not containing $(1,-1).$ The solution set is the region with BOTH shadings. The solution set is the region shaded GRAY
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