Study Guide
Graphing Systems of Inequalities

 

The solution of a system of inequalities is the set of all ordered pairs that satisfy both original inequalities. To find the solution of the sysem

{

y > x + 2

y ≤ −2x − 1

graph each inequality. The graph of each inequality is called a half-plane. The intersection of the half-planes represents the solution of the system. The graphs of y > x + 2  and  y ≤ −2x − 1 are the boundaries of the region.

 

Directions: Solve each system of inequalities by graphing.

1. y ≥ 2x

y ≥ −1

answer 1

2. 5x − 2y < 6

y > −x + 1

answer 2

3. |y| > x

answer 3

4. −x + y ≤ 6

x + y ≤ 2

answer 4

5. Write a system of inequalities for the graph at the right.

x + y ≤ 2  and  x > 1