Chapter 6.6, Problem 1P

Solve each system of inequalities by graphing.

$3x+y\le 1$

$x-y\le 3$

To determine

To solve: the given system of inequalities by graphing.

Explanation of Solution

Given information:

The given system of inequalities is

  $\begin{array}{l}3x+y.\le 1\\ x-y\le 3\end{array}$

Calculation:

Consider the system of equations

  $\begin{array}{l}3x+y.=1\Rightarrow \\ x=0\Rightarrow y=1\\ y=0\Rightarrow x=0.33\end{array}$

Draw the solid line passing through the points $(0,1)\&(0.33,0)$ and then shade the below

the region of the line.

  $\begin{array}{l}x-y=3\\ x=0\Rightarrow y=-3\\ y=0\Rightarrow x=3\end{array}$

Draw the solid line passing through the points $(0,-3)\&(3,0)$ and then shade the below

the region of the line.

Graph:

The graph of the given system is shown below

  

Hence, the overlapping region is the solution of the given inequalities.