3-3 SYSTEMS OF INEQUALITIES

Solve systems of linear inequalities by graphing and using

calculators.

Systems of Linear Inequalities

Two or more linear inequalities A solution to a system of linear

inequalities is an ordered pair that makes ALL of the inequalities in the system true.

We can use a graph to find these solutions

Graphing Systems Find the solutions to the system:

Graph each inequality in the same plane.

The overlap of each graph is the solution.

Writing a System of Inequalities

What system is represented by the graph below?

y < -x + 5 y ≥ x – 1

You Try!

What system of equations is represented by the graph?

y < -x + 1 y ≤ x + 1

Using a System of Inequalities You can spend at most 6 h playing basketball and

doing homework. You want to spend less than 2 h playing basketball. You must spend at least 1.5 h on homework. Draw a graph to show how you can spend your time.

First, define variables Write a system:

x + y ≤ 6 At most 6 hours playing and doing homework x < 2 Less than 2 hours playing y ≥ 1.5 At least 1.5 hours on homework

Graph the system

Calculators

To graph an inequality using a calculator, enter any equations using the Y= button.

Move to the far left of the equation where you should see a slash and press enter until you see: Shaded above

Shaded below

Then GRAPH

Assignment

Odds p.153 #11-15,21-25,55