Chapter 3.7, Problem 28WE

To determine

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

Answer to Problem 28WE

  

Explanation of Solution

Given information: The given inequality is:

  $\begin{array}{l}x-2y+2\ge 0(i)\\ x+2y-2\ge 0(ii)\end{array}$

Calculation: The given inequality is:

  $\begin{array}{l}x-2y+2\ge 0(i)\\ x+2y-2\ge 0(ii)\end{array}$ .

The corresponding equation is:

  $\begin{array}{l}x-2y=-2(iii)\\ x+2y=2(iv)\end{array}$

  $\begin{array}{l}x-2y=-2\\ \mathrm{put}x=0\\ 0-2y=-2\\ y=\frac{-2}{-2}=1\\ \mathrm{put}y=0\\ x-2(0)=-2\\ x-0=-2\\ x=-2\end{array}$

$x$	$0$	$-2$
$y$	$1$	$0$

  $\begin{array}{l}x+2y=2\\ \mathrm{put}x=0\\ 0+2y=2\\ y=\frac{2}{2}=1\\ \mathrm{put}y=0\\ x+2(0)=2\\ x+0=2\\ x=2\end{array}$

$x$	$0$	$2$
$y$	$1$	$0$

  

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

  $\begin{array}{l}0-2(0)+2\ge 0\\ 0-0+2\ge 0\\ 2\ge 0\end{array}$

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

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

  $\begin{array}{l}0+2(0)-2\ge 0\\ 0-0-2\ge 0\\ -2\ge 0\end{array}$

Which is false, therefore the closed half plane does not contain the origin is graph of given inequality.

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