Chapter 6.6, Problem 15PPE

To determine

To solve: the given system of inequalities using graphing.

Explanation of Solution

Given information:

The given system of inequalities is

  $\begin{array}{l}y\le -\frac{1}{3}x+7\\ y\ge -x+1\end{array}$

Calculation:

Find the intercepts

Consider the equation $y=-\frac{1}{3}x+7$

  $\begin{array}{l}y=0\Rightarrow x=21\\ x=0\Rightarrow y=7\end{array}$

Consider the equation $y=-x+1$

  $\begin{array}{l}y=0\Rightarrow x=1\\ x=0\Rightarrow y=1\end{array}$

Draw the solid line passing through the points $(1,0)\&(0,1)$ and shade below the line.

Draw the solid line passing through the points $(4,0)\&(0,-3)$ and shade above the line.

Graph:

The graph of given system of inequalities is shown below.

Hence, the common shaded region is the solution of the given system.