Here's one that's more complicated:

x + y is less than or equal to 8 ... y is less than or equal to x + 4 ... x is less than or equal to 5 ... x is greater than or equal to 0 ... y is greater than or equal to 0 Sure, it looks like a lot...  But, just take each line one at a time!

 

 

 

This combo means that we are in the first quadrant:

a graph with the first quadrant shaded

So, we just need to concentrate on that...

Here's the shaded area:

     *You should graph all this on your own on a separate piece of
      paper for the practice!

the points of intersection are ( 0 , 4 ) and ( 2 , 6 ) and ( 5 , 3 ) and ( 5 , 0 )

All the points of intersection need to be checked:

(0, 4) should be where

y = x + 4 ... x = 0

intersect...

Does the point work?

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(2, 6) should be where

y = x + 4 ... x + y = 8

intersect...

Does the point work?


(5, 3) should be where

x + y = 8 ... x = 5

intersect...

Does the point work?

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(5, 0) should be where

x = 5 ... y = 0

intersect...

This one obviously works!


YOUR TURN:

Graph and identify (and double check) all points of intersection:
 
-x + y is less than or equal to 2 ... x + y is less than or equal to 6 ... y is less than or equal to 3 ... y is greater than or equal to 0 ... x is greater then or equal to 0