## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 7 - Review Exercises - Page 878: 46

#### Answer

The graph is shown below: #### Work Step by Step

Let us consider the inequalities \begin{align} & 3x+2y\ge 6 \\ & 2x+y\ge 6 \end{align} Substitute the equals symbol in place of the inequality and rewrite the equation as given below: \begin{align} & 3x+2y=6 \\ & 2x+y=6 \end{align} To find the value of the x-intercept, substitute y = 0 as given below: \begin{align} & 3x+2y=6 \\ & 3x+2\times 0=6 \\ & 3x=6 \\ & x=2 \end{align} To find the value of the y-intercept, substitute x = 0 as given below: \begin{align} & 3x+2y=6 \\ & 3\times 0+2y=6 \\ & 2y=6 \\ & y=3 \end{align} To find another value of the x-intercept, substitute y = 0 as given below: \begin{align} & 2x+y=6 \\ & 2x+0=6 \\ & 2x=6 \\ & x=3 \end{align} To find another value of the y-intercept, substitute x = 0 as given below: \begin{align} & 2x+y=6 \\ & \left( 2\times 0 \right)+y=6 \\ & y=6 \end{align} Then, take origin $\left( 0,0 \right)$ as a test point and check the region in the graph to shade: \begin{align} & 3x+2y\ge 6\text{ and }2x+y\ge 6 \\ & 0\ge 6\text{ and }0\ge 6 \\ \end{align} As we see that both above expressions are incorrect, we know that the shaded region will not contain the test point; that is, the region away from the origin must be shaded. Thus, the graph of the given inequality is plotted and the solution set lies in the shaded region. After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.