1. Graphing A System Linear Inequalities

2. Objectives Define the solution for a system of inequalities
Find the solution of a system of inequalities

3. Solving a system of Inequalities
Consider the system
x + y ≥ -1 3 1 2 -1 -2 -3
-2x + y < 2

4. Solving a system of Inequalities
Consider the system
x + y ≥ -1
y≥-x-1 3 1 2 -1 -2 -3
-2x + y < 2

5. Solving a system of Inequalities
Consider the system
x + y ≥ -1 3 1 2 -1 -2 -3
-2x + y < 2
y<2x+2

6. 3 1 2 -1 -2 -3 3 1 2 -1 -2 -3
x + y ≥ -1
-2x + y < 2

7. Solving a system of Inequalities
Consider the system
x + y ≥ -1 3 1 2 -1 -2 -3
-2x + y < 2
SOLUTION:
Lies where the two shaded
regions intersect each
other.

8. Solving a system of Inequalities
Consider the system
-2x + 3y < -6
Graph 3 1 2
5x + 4y < 12
y < x - 2 2 3 3 2 4 -1 -2 1 -1 -2

9. Solving a system of Inequalities
Consider the system
-2x + 3y < -6 3 1 2
5x + 4y < 12
Graph
y < x + 3 5 4 3 2 4 -1 -2 1 -1 -2

10. Solving a system of Inequalities
Consider the system
-2x + 3y < -6 3 1 2
5x + 4y < 12
Graph
SOLUTION: 
(0,0)
Lies where the two shaded
regions intersect each
other. 3 2 4 -1 -2 1 -1 -2
Hidden word: juice

11. Solving a system of Inequalities
Consider the system
-2x + 3y < -6 3 1 2
5x + 4y < 12
Graph
NOTE: 
(0,0)
All order pairs in dark
region are true in both
inequalities. 3 2 4 -1 -2 1 -1 -2

12. Solving a system of Inequalities
Consider the system 10 8 12 6 4 2 -2 -4 -6
x - 4y ≤ 12
Graph
4y + x ≤ 12
TEST: (0,0)
(0,0)
(0) - 4(0) ≤ 12
0 - 0 ≤ 12 
0 ≤ 12

13. Solving a system of Inequalities
Consider the system 10 8 12 6 4 2 -2 -4 -6
x - 4y ≤ 12
4y + x ≤ 12
Graph
TEST: (0,0)
(0,0)
4(0) + (0) ≤ 12 
0 ≤ 12

14. Now you try
When you have finished the work make sure to fill out a document. Find the hidden word with in the power point and write it next to your name.