Question 82579
Solve the first equation for y:


{{{x-2y<4}}}


{{{-2y<4-x}}} Subtract x from both sides


{{{y>(1/2)x-2}}} Divide both sides by -2. Remember multiplying or dividing by a negative flips the inequality sign



Now graph both {{{y=(1/2)x-2}}} and {{{x=4}}}

{{{ graph( 300, 200, -6, 5, -10, 10, (1/2)x-2, 10000(x-4)) }}}


Lets pick a test point (0,0) and test it with {{{y>(1/2)x-2}}}


{{{(0)>(1/2)(0)-2}}} Plug in x=0, y=0


{{{0>-2}}} Since this expression is true we shade the entire region containing (0,0) for the inequality {{{y>(1/2)x-2}}}. This region is above the line.


<a href="http://photobucket.com" target="_blank"><img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/step1.jpg" border="0" alt="Photo Sharing and Video Hosting at Photobucket"></a>


Now lets test {{{x<4}}} 


{{{x<4}}} Plug in x=0


{{{0<4}}} Since this expression is true we shade the entire region containing (0,0) for the inequality {{{x<4}}}. This is the region to the left of the vertical line.

<a href="http://photobucket.com" target="_blank"><img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/step2.jpg" border="0" alt="Photo Sharing and Video Hosting at Photobucket"></a>


Notice how these regions overlap. This overlapping region is our final shaded region. Every point in this region satisfies both {{{y>(1/2)x-2}}} and {{{x<4}}}

<a href="http://photobucket.com" target="_blank"><img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/final.jpg" border="0" alt="Photo Sharing and Video Hosting at Photobucket"></a>