Chapter 3.7, Problem 44WE

To determine

To graph: The given system of inequalities.

Explanation of Solution

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

Graph:

To plot the graph, using the associated equality $\left|y\right|=\left|x\right|$ , the graph $\left|y\right|=\left|x\right|$ is the lines $x=y$ and $x=-y$ .

Now checking which out of the left, right, above and below regions are included in the graph by checking if points satisfy the inequality,

Left: $(-5,0)$ , $\left|0\right|\le \left|-5\right|\to True$

Right: $(5,0)$ , $\left|0\right|\le \left|5\right|\to True$

Above: $(0,5)$ , $\left|5\right|\le \left|0\right|\to False$

Below: $(0,-5)$ , $\left|-5\right|\le \left|0\right|\to False$

  $\therefore$ Only left and right regions are included in the graph of system of equations,

  

Interpretation:

The graph of system forms rotated $X-shape$ in which boundary lines are included.