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

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

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

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)

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.

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.

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

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

Homework 488+489/59-63 odd

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