Soppose you have 

4x+y > 5
2x-y > 3

Solve each for y

y > 5 - 4x
y < 2x - 3

Press Y=

To the right of \Y1= type 5-4x

To the right of \Y2= type 2x-3

Now press ZOOM then 6 and you will see two
lines graphed.

But you want them shaded.  

Press Y= again

Now you have to learn about the back-slash
 \ that you see to the left of Y1 and Y2.
 
Use the left arrow key to get the cursor 
onto that \ left of Y1

Since the first inequality begins with 

y >
                                           _ 
Press ENTER ENTER and the \ will turn into \|.
I can't draw it but it's a blinking triangle 
showing shading above a diagonal line.
   
Next use the left arrow key to get the cursor 
onto that \ left of Y2

Since the second inequality begins with 

y <
                                            
Press ENTER ENTER ENTER and the \ will turn into |\,
blinking a triangle shaded below a diagonal line.

Now press GRAPH and it will shade above the first line with 
vertical lines, and below the second kind with a horizontal
line.  The the region which has both vertical and horizontal
shading is the solution.

Edwin