3.4 Solving Systems of Linear Inequalities

Objectives: Write and graph a system of linear inequalities in two variables.

Write a system of inequalities in two variables for a given solution region.

Standard: 2.8.11.K. Apply an appropriate technique to graph a linear inequality in two

variables.

• A system of linear inequalities is a collection of linear inequalities that use the same variables.

• The solution is any ordered pair that makes each of the inequalities in the system a true statement.

• When graphing a system of linear inequalities, shade the part of the graph where all of the solution regions for each individual linear inequality overlap.

* b. x ≥ 0 y ≥ 0 y > -x + 2 y ≤ -2x + 3

C.

* d. y > -x – 2 y > x + 3 y ≤ 3

Ex 2. Graph each inequality in a coordinate plane.

• a. –3 ≤ x ≤ 2

b. –1 < y < 3

* c. 0 < x ≤ 4

* d. 1 ≤ y < 4

Writing Activities

PSSA Warm-Up QuestionAlg II – Chp. 3

• Standard 2.8.11 G Analyze and explain systems of equations and inequalities.

Solve this system of inequalities:

2x + y < 5 y < x - 4

HomeworkPg. 183-184 #10-44 even