Chapter 3.7, Problem 45WE

To determine

To graph:The given system of inequalities.

Explanation of Solution

Given information:System is: $\left|x\right|+\left|y\right|\le 2$ .

Graph:

When both are positive,

  $\begin{array}{l}x+y\le 2\\ y\le -x+2\end{array}$

When $x$ is negative and $y$ is positive,

  $\begin{array}{l}-x+y\le 2\\ y\le x+2\end{array}$

When $x$ is positive and $y$ is negative,

  $\begin{array}{l}x-y\le 2\\ y\ge x-2\end{array}$

When $x$ is negative and $y$ is also negative,

  $\begin{array}{l}-x-y\le 2\\ y\ge -x-2\end{array}$

Considering the respective individual associated equations and solving them for $y$ and further plotting them, the common region i.e. the graph of system is shown below,