Chapter 6.6, Problem 20PPE

To determine

To solve: the given system of inequalities using graphing.

Explanation of Solution

Given information:

The given system of inequalities is

  $\begin{array}{l}2x-\frac{1}{4}y<1\\ 4x+8y>4\end{array}$

Calculation:

Find the intercepts

Consider the equation $2x-\frac{1}{4}y=1$

  $\begin{array}{l}y=0\Rightarrow x=0.5\\ x=0\Rightarrow y=-4\end{array}$

Consider the equation $4x+8y=4$

  $\begin{array}{l}y=0\Rightarrow x=1\\ x=0\Rightarrow y=0.5\end{array}$

Draw the dashed line passing through the points $(0.5,0)\&(0,-4)$ and shade below the line.

Draw the dashed line passing through the points $(1,0)\&(0,0.5)$ 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.