Chapter 3.7, Problem 26WE

To determine

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

Answer to Problem 26WE

  

Explanation of Solution

Given information: The given inequality is:

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

Calculation: The given inequality is:

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

The corresponding equation is:

  $\begin{array}{l}x+y=0(iii)\\ x+y=2(iv)\end{array}$

  $\begin{array}{l}x+y=0\\ \mathrm{put}x=0\\ 0+y=0\\ y=0\\ \mathrm{put}y=1\\ x+1=0\\ x=-1\end{array}$

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

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

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

  

Put $x=1\mathrm{and}y=1$ in equation $(i)$ we get:

  $\begin{array}{l}1+1>0\\ 2>0\end{array}$

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

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

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

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

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

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

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