1. 7.6 Graphing Systems of Linear Inequalities
Algebra
7.6
Graphing Systems of
Linear Inequalities

2. REVIEW: Graph of Linear Inequality
Looks like this (shaded half-plane)
The solutions are all the points in the shaded region

3. Graph of System of Linear Inequalities
Looks like this (shaded region between two lines)
The solutions are all the points in the shaded region

4. Shade the overlap
To shade above both lines

5. Shade the overlap
To shade above one line and below the other

6. Shade the overlap
To shade above one line and below the other

7. Shade the overlap
To shade below both lines

8. Steps to Graphing
Graph the lines for each linear inequality in the same plane.
Locate half-plane to shade for each line (above or below).
The region that is overlapping (in both solution areas) is the one to shade.

9. Example Graph the system: y < 3 y > 1
The solution region is below the line
y = 3
and above the line y = 1.

10. Example Graph the system: y < ½ x + 1 y > ½ x - 2
The solution region is below the line
y = ½ x + 1
and above the line y = ½ x - 2

11. Example Graph the system: y < -½ x + 1 y ≥ ½ x - 1
The solution region is above the line
y = ½ x - 1
and below the line y = -½ x + 1

12. Example Graph the system: y > -x - 1 y ≥ 2x - 8
The solution region is above the line
y = 2x - 8
and above the line y = -x - 1

13. Example Graph the system: x > -3 y < 1 y > x - 2
VERTICAL
HORIZONTAL
The solution region is right of the line
x = -3
below the line
y = 1
and above the line y = x - 2

14. Homework
pg # 9-22