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Systems of Inequalities

Ok, now let's do a system:

x + y is less than or equal to 3

x > -1

We just graph each one and see where they overlap.

the graph of x + y is less than or equal to 3 ... the portion of the graph under the line is shaded  the graph of x > -1 ... the portion of the graph to the right of the line is shaded

What will the intersection look like?

 

Knowing what this point is is going to be really important in the next section!

It LOOKS like it's (-1, 4), but we need to be sure.  Remember that the point of intersection is the solution to the system

stick the x = -1 into x + y = 3 for x

 a graph of x + y is less than or equal to 3 and x > -1 ... the shaded portion is to the right of the x = -1 and below x + y = 3

We have the x guy, so stick him into the other equation:

x + y = 3 ... -1 + y = 3 ... y = 4

Yep, the point is (-1, 4), so here's our official answer:

a graph ... the point of intersection of the two lines is ( -1 , 4 )
 

YOUR TURN:

Graph x + y < 4

x - y is greater than or equal to -2