In this section you will focus on solving linear systems using inequalities, ( > < ) This is known as Linear Systems of Inequalities. Two or more inequalities form a system, and the solution is an ordered pair that is the answer to the inequality graphed. As you can see, it all comes together and makes sense once the solution is solved and graphed.

Examples: y<2 inequality 1

x > -1 inequality 2

y > x - 2 inequality 3

 

Example graphed:

Graphing a System of Linear Inequalities

1. Sketch the line that correspnds to the inequality.

2. Shade the plane or portion of the graph that each inequality corresponds to.

3. The intersection of the shaded planes is the solution of the graph.

Now try some of these problems own your own. Good Luck!

a. ( 2x + y < 4

( x + 2y > - 4

b. ( x + 2y < 4

( - x + 2y < 4

c. ( x + y < 1

( - x + y > 1

d. ( x + y < 5

( x > 2

( y > 0