Over Lesson 6–5. Splash Screen Solving Systems of Inequalities Lesson 6-6.

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Presentation transcript:

Over Lesson 6–5

Splash Screen Solving Systems of Inequalities Lesson 6-6

Then/Now You graphed and solved linear inequalities. Solve systems of linear inequalities by graphing.

Vocabulary system of inequalities – a set of two or more inequalities with the same variables.

Example 1 Solve by Graphing 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 solution. The graph of y = – x – 3 is solid and is included in the graph of the solution.

Example 1 Solve the system of inequalities by graphing 2x + y ≥ 4 and x + 2y > –4. A.B. C.D.

Example 2 No Solution 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.

Example 2 Solve the system of inequalities by graphing. y > 4x y < 4x – 3 A. y > 4x B. all real numbers C. D. y < 4x

Example 3 Whole-Number Solutions A. 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. Define the variables and write a system of inequalities to represent this situation. Then graph the system. Let g = grade point average. So, g ≥ 3.0. Let v = the number of volunteer hours. So, v ≥ 10.

Example 3 Whole-Number Solutions Answer: The system of inequalities is g ≥ 3.0 and v ≥ 10.

Example 3 Whole-Number Solutions B. 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. Name one possible solution. Answer: One possible solution is (3.5, 12). A grade point average of 3.5 and 12 hours of volunteering meet the requirements of the college service organization.

Example 3 A.B. C.D. A. 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.

Example 3 A.(16, 115) B.(17, 105) C.(17, 125) D.(18, 108) B. The senior class is sponsoring a blood drive. Anyone who wished to give blood must be at least 17 years old and weigh at least 110 pounds. Choose one possible solution.

End of the Lesson Homework Page 374 #9, 25 And Chapter 6 Review