1. Review: 8.5a Mini-Quiz
1. Solve the system of inequalities by graphing. {
2. Write a system of inequalities that describes the green region.

2. Class Greeting

3. Objective: Students will solve real world word problems by graphing systems of linear inequalities in two variables.

4. Chapter 8 Systems of Linear Equations and Inequalities
Lesson 8-5b
Systems of Linear Inequalities

5. Example 1 – Target Heart Rate
A person’s maximum heart rate is 220 – x, where x is the person’s age in years (20  x  70). It is recommended that during exercise a person strives for a heart rate that is at least 50% of the maximum and at most 75% of the maximum. Write a system of linear inequalities that describes the target heart rate zone, and sketch a graph of the system.
(Source: American Heart Association)

6. Example 1 – Target Heart Rate
continued
Solution
Let y represent the person’s heart rate.
From the given information, you can write the following
system of inequalities.
x  20
x  70
y  0.50(220 – x)
y  0.75(220 – x)
To graph this system, sketch the half-planes represented
by the four linear inequalities.
Person’s age must be at least 20.
Person’s age can be at most 70.
Target rate is at least 50% of maximum rate.
Target rate is at most 75% of maximum rate.

7. Example 5 – Target Heart Rate
continued
As shown in the figure, the region that is common to all four of these half-planes is a four-sided polygon.

8. Lesson Summary: Objective: Students will solve real world word problems by graphing systems of linear inequalities in two variables.

9. Preview of the next Lesson: Objective: Students will learn how to solve a system of linear equations using substitution. .

10. Homework
/59-63 odd

11. Stand Up Please