Chapter 6.6, Problem 13PPE

To determine

To solve: given system of inequalities by graphing.

Explanation of Solution

Given information: a system of inequalities is given as follows-

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

Graph:

  

Interpretation:

In order to draw the graph of $y\le -x+4$ we have to first draw the line $y=-x+4$ . This divides $xy$ -plane into two regions. We can check the region which describes $y\le -x+4$ by simply putting value of any point of that region in the given inequality.

Similarly we can draw the graph of $y>\frac{1}{4}x$ .

The common shaded region is solution graph of given system of inequalities.