1. Section 3.3 - Graphing and Solving Systems of Linear Inequalities
ALGEBRA TWO
CHAPTER THREE: SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES
Section Graphing and Solving Systems of Linear Inequalities

2. LEARNING GOALS
Goal One - Graph a system of linear inequalities to find the solutions of the system.
Goal Two - Use systems of linear inequalities to solve real- life problems.

3. Graphing a System of Linear Inequalities
The following is a system of linear inequalities in two variables:
x + y < 6 Inequality 1
2x - y > 4 Inequality 2
A solution of a system of linear inequalities is an ordered pair that is a solution of each inequality in the system.
The graph of a system of linear inequalities is the graph of all solutions of the system. 1

4. Graphing a System of Linear Inequalities
To graph a system of linear inequalities, do the following for each inequality in the system:
STEP 1: Graph the line that corresponds to the inequality. Use a dashed line for and inequality with < or > and a solid line for an inequality with < or >.
STEP 2: Lightly shade the half-plane that is the graph of the inequality. Colored pencils may help you distinguish the different half-planes.
The graph of the system is the region common to all of the half-planes. If you used colored pencils, it is the region that has been shaded with every color. 1

5. Graphing a System of Linear Inequalities
Graph the linear inequality system:
Inequality y > -3x - 1
Inequality y < x + 2
y > -3x - 1
The purple area represents all solutions for this linear inequality.
y < x + 2 1

6. ASSIGNMENT
READ & STUDY: pg
WRITE: pg #13, #15, #17, #19, #27, #31, #37, #39, #41