Hello, newgirl2012!
[I assume you want to graph this region.]
. . $\displaystyle \begin{array}{cc}(1) & x \:\ge\: 3 \\
(2) & y \:\ge\: 2 \\ (3) & 2x+y \:\le\: 2 \end{array}$
$\displaystyle (1)\;x \:\ge\:3$
Graph the vertical line $\displaystyle x = \text{}3$
Then shade region to the right of that line.
Code:
://// 
://// 
://// 
://// 
://// 
:////+
://// 
://// 
://// 
$\displaystyle (2)\;y \,\ge\,\text{}2$
Graph the horizontal line $\displaystyle y = \text{}2$
Then shade the region above that line.
Code:

//////////
//////////
//////////
/////+/////
//////////
//////////
//////////
     +    


$\displaystyle (3)\;2x + y \:\le\:2 $
Graph the line $\displaystyle y\:=\:2x2$
. . It has intercepts $\displaystyle (1,\,0)\text{ and }(0,2)$
Then shade the region below that line.
Code:
:\ 
::\ 
:::\ 
::::\ 
:::::\ 
::::::*+
:::::::\ 
:::::::\ 
::::::::\
::::::::*
:::::::\
:::::::\
::::::::\
Now consider the region that has been shaded three times.
Code:
\ 
* 
:\ 
::\ 
:::\ 
::::\+
:::::\ 
::::::\ 
:::::::\
*    *

That is the solution!