Chapter 3.7, Problem 27WE

To determine

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

Answer to Problem 27WE

  

Explanation of Solution

Given information: The given inequality is:

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

Calculation: The given inequality is:

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

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:

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

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

Draw as a dashed line because the inequality $<\mathrm{and}\mathrm{not}\le$ .

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

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

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

Draw as a dashed line because the inequality $>\mathrm{and}\mathrm{not}\ge$ .

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