Chapter 6.6, Problem 16PPE

To determine

To solve: the given system of inequalities using graphing.

Explanation of Solution

Given information:

The given system of inequalities is

  $\begin{array}{l}x+2y\le 10\\ x+2y\ge 9\end{array}$

Calculation:

Find the intercepts

Consider the equation $x+2y=10$

  $\begin{array}{l}y=0\Rightarrow x=10\\ x=0\Rightarrow y=5\end{array}$

Consider the equation $x+2y=9$

  $\begin{array}{l}y=0\Rightarrow x=9\\ x=0\Rightarrow y=4.5\end{array}$

Draw the solid line passing through the points $(9,0)\&(0,4.5)$ 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.