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: 68

Answer

$ x^{2}+y^{2} \leq 25$ $x+2y \geq 5 $ .
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Work Step by Step

First sentence: $\quad x^{2}+y^{2} \leq 25 $ Second sentence: $\quad x+2y \geq 5 $ 1st inequality ($ \leq $ inequality sign, border solid):: $x^{2}+y^{2} = 25$ is a circle, centered at (0,0), radius 5. Test point: (0,0). $\quad $Is $ 0^{2}+0^{2} \leq 25 \quad ?$ Yes. shade the region containing (0,0). 2nd inequality ($ \geq$ inequality sign, border solid): Graph $x+2y = 5:$ $2y=-x+5$ $y=-\displaystyle \frac{1}{2}x+\frac{5}{2}$ y intercept=$\displaystyle \frac{5}{2}$, and for x=5, y=$0$ . Draw the line through (0,$\displaystyle \frac{5}{2}$) and ($5,0$) Test point: (0,0). $\quad $Is $0+2(0) \geq 5 ?$ No. shade the region not containing (0,0). The solution set is the region with both shadings. (grey on the screenshot)
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