1. Systems of Inequalities (6-8)
Objective: Graph systems of inequalities. Solve systems of linear inequalities by graphing.

2. Systems of Inequalities
A set of two or more inequalities with the same variables is called a system of inequalities.
The solution of a system of inequalities with two variables is the set of ordered pairs that satisfy all of the inequalities in the system.
The solution set is represented by the overlap, or intersection, of the graphs of the inequalities.

3. Example 1 Solve the system of inequalities by graphing. y < 2x + 2
The line y < 2x + 2 is a dashed line.
The line y ≥ -x – 3 is a solid line.

4. Check Your Progress Choose the best answer for the following.
Solve the system of inequalities by graphing 2x + y ≥ 4 and x + 2y > -4. A. B. C. D.

5. No Solution Sometimes the regions never intersect.
When this happens, there is no solution because there are no points in common.

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

7. Check Your Progress Choose the best answer for the following.
Solve the system of inequalities by graphing.
y > 4x
y < 4x – 3
all real numbers 
y < 4x

8. Apply Systems of Inequalities
When using a system of inequalities in a real-world problem, sometimes only whole-number solutions will make sense.

9. Example 3
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.
x ≥ 3.0
y ≥ 10
Name one possible solution.
Any point in the double shaded region is a solution.
3.5 grade point average and hours volunteering.

10. Check Your Progress Choose the best answer for the following.
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.
x ≥ 17
y ≥ 110 A. B. C. D.

11. Check Your Progress Choose the best answer for the following.
Choose one possible solution.
(16, 115)
(17, 105)
(17, 125)
(18, 108)