Study Guide: Graphing Systems of Inequalities

These web-based activities were developed, during summer sessions from 1997 through 1999, by students at Mainland High School, located in Daytona Beach, FL. As part of Mainland's CCTT grant, the students were given permission by the book's publisher to convert the ancillary materials of the County's adopted Algebra 1 textbook (Glencoe Algebra 1 — ISBN: 9780028253282) into html format.

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