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4. Contents Lesson 7-5Graphing Systems of Inequalities

5. Lesson 5 Contents Example 1Solve by Graphing Example 2No Solution Example 3Use a System of Inequalities to Solve a Problem Example 4Use a System of Inequalities

6. The solution includes the ordered pairs in the intersection of the graphs ofand The region is shaded in green. The graphs andare boundaries of this region. The graph is dashed and is not included in the graph of. The graph ofis included in the graph of Example 5-1a Solve the system of inequalities by graphing. Answer:

7. Example 5-1b Solve the system of inequalities by graphing. Answer:

8. Example 5-2a Answer: Solve the system of inequalities by graphing. The graphs ofand are parallel lines. Because the two regions have no points in common, the system of inequalities has no solution.

9. Example 5-2b Solve the system of inequalities by graphing. Answer: Ø

10. Example 5-3a Service A college service organization requires that its members maintain at least a 3.0 grade point average, and volunteer at least 10 hours a week. Graph these requirements. Words The grade point average is at least 3.0. The number of volunteer hours is at least 10 hours. Variables If the grade point average and the number of volunteer hours, the following inequalities represent the requirements of the service organization.

11. Example 5-3a Inequalities The grade point average is at least 3.0. The number of volunteer hours is at least 10. The solution is the set of all ordered pairs whose graphs are in the intersection of the graphs of these inequalities. Answer:

12. Example 5-3b The senior class is sponsoring a blood drive. Anyone who wishes to give blood must be at least 17 years old and weigh at least 110 pounds. Graph these requirements. Answer:

13. Example 5-4a Employment Jamil mows grass after school but his job only pays $3 an hour. He has been offered another job as a library assistant for $6 per hour. Because of school, his parents allow him to work 15 hours per week. How many hours can Jamil mow grass and work in the library and still make at least $60 per week? Letthe number of hours spent mowing grass and the number of hours spent working in the library. Since g and both represent a number of days, neither can be a negative number. The following system of inequalities can be used to represent the conditions of this problem.

14. Example 5-4a The solution is the set of all ordered pairs whose graphs are in the intersection of the graphs of these inequalities. Only the portion of the region in the first quadrant is used sinceand. Answer: Any point in the region is a possible solution. For example (2, 10) is a point in the region. Jamil could mow grass for 2 hours and work in the library for 10 hours during the week.

15. Example 5-4b Emily works no more than 20 hours per week at two jobs. Her baby- sitting job pays $3 an hour and her job as a cashier at the bookstore pays $5 per hour. How many hours can Emily work at each job to earn at least $80 per week? Answer: number of hours baby sitting number of hours working as a cashier

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17. Algebra1.com Explore online information about the information introduced in this chapter. Click on the Connect button to launch your browser and go to the Algebra 1 Web site. At this site, you will find extra examples for each lesson in the Student Edition of your textbook. When you finish exploring, exit the browser program to return to this presentation. If you experience difficulty connecting to the Web site, manually launch your Web browser and go to www.algebra1.com/extra_examples.

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