3-3 Graphing and Solving Systems of Linear Inequalities Objective: Students will be able to graph a system of inequalities to find the solutions of the.

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3-3 Graphing and Solving Systems of Linear Inequalities Objective: Students will be able to graph a system of inequalities to find the solutions of the system.

The following is a system of linear inequalities. 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.

Graphing a System of Linear Inequalities 1. Graph the boundary line that corresponds to the inequality. Use a dashed lined for an inequality with and a solid line for  or . 2. Lightly shade in the half-plane that is the graph of the inequality. Colored pencils may help you distinguish the different half-planes.

Example 1: Graph the system

Step 1: Graph the boundary line for each equation.

y > -3x + 1 y < x + 2

Determine the half planes that make the inequalities true. Choose a test point (0, 0)

Example 2: Graph the system

Example 3 Writing and using a system of Inequalities Heart Rate: A person’s theoretical maximum heart rate is 220 – x where x is the person’s age in years (20  x  65). When a person exercises, it is recommended that the person strive for a heart rate that is at least 70% and at most 85% of the maximum.

a.You are making a poster for the health class. Write and graph a system of linear inequalities that describes the information given above. b.A 40- year old person has a heart rate of 150 (heart beat per minute) when exercising. Is the person’s heart rate in the target zone?

Solution: Let y represent the person’s heart rate. From the given information, you can write the following inequalities

Solve: This determines the lower limit of the target zone.

This determines the upper limit of the target zone.

b. From the graph you can see that the target zone for a 40 year-old person is between 126 and 153. A 40 year-old person who has a heart rate of 150 is within the target zone.

Homework page 159, 12 – 46 even, 51-54, 67 – 77 odd

Turn to page 156 in your book. Investigating Graphs of Systems of Inequalities. Work in groups. Stay on task. You will have 10 minutes to complete the task. a) Region 1 b) Region 3 c) Region 4 d) Region 2