1. Mathematical Practices
Content Standards
A.REI.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
6 Attend to precision.
CCSS

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

3. Solve the system of inequalities by graphing. y < 2x + 2
Solve by Graphing
Solve the system of inequalities by graphing.
y < 2x + 2
y ≥ – x – 3
Example 1

4. Solve the system of inequalities by graphing. y < 2x + 2
Solve by Graphing
Solve the system of inequalities by graphing.
y < 2x + 2
y ≥ – x – 3
Example 1

5. Solve the system of inequalities by graphing 2x + y ≥ 4 and x + 2y > –4.
Example 1

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

7. Solve the system of inequalities by graphing. y ≥ –3x + 1 y ≤ –3x – 2
No Solution
Solve the system of inequalities by graphing.
y ≥ –3x + 1
y ≤ –3x – 2
Answer:
Example 2

8. Solve the system of inequalities by graphing. y ≥ –3x + 1 y ≤ –3x – 2
No Solution
Solve the system of inequalities by graphing.
y ≥ –3x + 1
y ≤ –3x – 2
Example 2

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

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

11. Let g = grade point average. So, g ≥ 3.0.
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

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

13. 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.
Example 3

14. 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.
Example 3

15. A. The senior class is sponsoring a blood drive
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.
A. B.
C. D.
Example 3

16. A. The senior class is sponsoring a blood drive
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.
A. B.
C. D.
Example 3

17. B. The senior class is sponsoring a blood drive
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.
A. (16, 115)
B. (17, 105)
C. (17, 125)
D. (18, 108)
Example 3

18. B. The senior class is sponsoring a blood drive
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.
A. (16, 115)
B. (17, 105)
C. (17, 125)
D. (18, 108)
Example 3

19. End of the Lesson