1. Lesson 8 Menu Five-Minute Check (over Lesson 6-7) Main Ideas and Vocabulary California Standards Example 1: Solve By Graphing Example 2: Use a System of Inequalities

2. Lesson 8 MI/Vocab system of inequalities Solve systems of inequalities by graphing. Solve real-world problems involving systems of inequalities.

3. Lesson 8 CA Standard 9.0 Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets. (Key, CAHSEE)

4. Lesson 8 Ex1 Solve By Graphing A. Solve the system of inequalities by graphing. y < 2x + 2 y ≥ – x – 3 Answer: The solution includes the ordered pairs in the intersection of the graphs of y < 2x + 2 and y ≥ – x – 3. The region is shaded in green. The graphs y = 2x + 2 and y = – x – 3 are boundaries of this region. The graph y = 2x + 2 is dashed and is not included in the graph of y < 2x + 2. The graph of y = – x – 3 is included in the graph of y ≥ – x – 3. Animation: Solving Systems of Equations by Graphing

5. Lesson 8 Ex1 Solve By Graphing B. Solve the system of inequalities by graphing. y ≥ –3x + 1 y ≤ –3x – 2 Answer: The graphs of y = –3x + 1 and y = –3x – 2 are parallel lines. Because the two regions have no points in common, the system of inequalities has no solution.

6. A.A B.B C.C D.D Lesson 8 CYP1 A. Solve the system of inequalities by graphing 2x + y ≤ 4 and x + y > –4. A.B. C.D.

7. A.A B.B C.C D.D Lesson 8 CYP1 B. Solve the system of inequalities by graphing. y > 4x y < 4x – 3 A. y > 4x B. all real numbers C. D. cannot be determined

8. Lesson 8 Ex2 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 g = the grade point average and v = the number of volunteer hours, the following inequalities represent the requirements of the service organization. Use a System of Inequalities

9. Lesson 8 Ex2 Inequalities The grade point average is at least 3.0. g ≥ 3.0 Answer: The solution is the set of all ordered pairs whose graphs are in the intersection of the graphs of these inequalities. Use a System of Inequalities The number of volunteer hours is at least 10. v ≥ 10

10. Lesson 8 CYP2 1.A 2.B 3.C 4.D 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. A.B. C.D.

11. End of Lesson 8