1. Algebra 1
Section 7.8

2. Systems of Inequalities
When you graph an inequality, the shaded region represents all possible solutions.
The solution to a system of inequalities consists of the ordered pairs that satisfy all the inequalities of the system.

3. Solving a System of Inequalities
Graph all inequalities on the same set of axes.
Find the solution set where the shaded regions intersect.
Check the result.

4. Shade above dashed line
Example 1
3x + y > x – y ≤ 8
y > -3x y ≥ x – 8
y-intercept: (0, 4)
m = -3
Shade above dashed line
y-intercept: (0, -8)
m = 1
Shade above solid line

5. Example 1
3x + y > x – y ≤ 8

6. Example 2 Begin with the first two inequalities. x > 0 y > 0
Shade to the right of the dashed line
x = 0.
Shade above the dashed line y = 0.

7. The first two inequalities limit our solutions to the first quadrant.
Example 2
The first two inequalities limit our solutions to the first quadrant.

8. Example 2 Now graph the third inequality. 2x – y > 1 y < 2x – 1
y-int: (0, -1)
m = 2
Shade below dashed line

9. Systems of Inequalities
Sometimes we are given the graph and can write the system of inequalities which it represents.
Begin by finding the equations of the boundary lines.

10. Example 3 The orange line is horizontal. y = -4
Since the line is solid and the shading is above it,
y ≥ -4

11. Example 3 The blue line has a slope of -3 and a y-intercept of 1.
y = -3x + 1
Since the line is solid and the shading is below it,
y ≤ -3x + 1

12. Homework: pp