6-6 Systems of Linear Inequalities Goal: Solve a system of linear inequalities by graphing. Eligible Content: A1.1.3.2.1 / A1.1.3.2.2

Vocabulary System of Linear Inequalities – two or more inequalities with the same variables. Solution – any ordered pair that works in the system of inequalities.

Solutions The solution is the shaded area! There are many solutions to every system! All of the ordered pairs inside the shaded area are solutions!

Steps Get each y alone. Graph each inequality on the same coordinate plane. Shade the area that the inequalities have in common.

Remember: Solid line  ≤ and ≥ Dotted line  < and > Shade above  > and ≥ Shade below  < and ≤

What your graphs will look like:

Let’s Practice Shading!! y -x + 5 y 1 3 x – 1

Examples 1. 2. 3. 4. 5.

Solve the system of inequalities by graphing 2x + y ≥ 4 and x + 2y > –4. GREEN AREA is solution A. B. C. D.

Solve the system of inequalities by graphing. y > 4x y < 4x – 3 A. y > 4x B. all real numbers C. D. y < 4x

Practice 1. 2. 3. 4.

Homework Page 374 #10-20 even