Chapter 3.7, Problem 19WE

To determine

To draw: The graph of given inequality in a coordinate plane.

Answer to Problem 19WE

  

Explanation of Solution

Given information: The given inequality is:

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

Calculation: The given inequality is:

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

The corresponding equation is:

  $\begin{array}{l}y=2(i)\\ y=x(ii)\end{array}$

Graph of equation is equation $(i)$ is parallel to $x-$ axis and $2$ unit up the $x-$ axis.

  $\begin{array}{l}y=x\\ \mathrm{put}x=0\\ y=0\\ \mathrm{put}y=1\\ x=1\end{array}$ v.

$x$	$0$	$1$
$y$	$0$	$1$

  

Put $x=0\mathrm{and}y=0$ in equation $(i)$ we get:

  $0\le 2$

Which is true, therefore the closed half plane containing the origin is graph of given inequality.

Put $x=0\mathrm{and}y=0$ in equation $(ii)$ we get:

  $0\ge 0$

Which is true, therefore the closed half plane containing the origin is graph of given inequality.

Thus the common shaded region is the graph of all inequality.