## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 7 - Section 7.5 - Systems of Inequalities - Exercise Set - Page 864: 78

#### Answer

Both equations are satisfied by the coordinates of point B, which means that the provided point lies in the healthy weight region.

#### Work Step by Step

The point B has coordinates $\left( 76,220 \right)$. So, in order to check whether this point lies in the healthy weight region or not, substitute the coordinates of point B for x and y variables respectively in both the provided equations as shown below: Put the values in the first equation as given below: \begin{align} & 5.3x-y\ge 180 \\ & 5.3\left( 76 \right)-220\ge 180 \\ & 182.8\ge 180 \end{align} And the inequality holds. Now, put the values in the second equation as given below: \begin{align} & 4.1\left( x \right)-y\le 140 \\ & 4.1\left( 76 \right)-220\le 140 \\ & 91.6\le 140 \end{align} Here also the inequality holds. Thus, both equations are satisfied by the coordinates of point B, which means that the provided point lies in the healthy weight region.

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