1. 3.3 Systems of Inequalities

2. In Chapter 2 we learned how to graph a two variable inequality
Graph the inequality
y > -x + 2

3. What would happen if we graph more than one inequality at the same time?
Graph the inequality
y > -x + 2
Let’s add y<2
Notice that the inequalities overlap. When the inequalities overlap we want to see if we can get a common boundary. This boundary represents the solution to the set of inequalities.

4. Ex: GRAPHING INEQUALITIES
(8 , 2)
x + y ≥ -1
x – y ≤ 6
y ≤ 2
y ≥ -x – 1
y ≥ x – 6
y ≤ 2
(-3 , 2)
Note where the three inequalities overlap. This forms a boundary known as the Feasible Region.
Also note where the boundaries intersect. The points where the boundary lines intersect, or change direction is called a constraint point.
(2.5 , -3.5)

5. Ex: GRAPHING INEQUALITIES
1 ≤ y ≤ 5
x + y ≤ 8
2 ≤ x and x ≤ 6
1 ≤ y and y ≤ 5
y ≤ -x + 8
(3, 5)
(6, 2)
(2, 5)
Sometimes your feasible region can seem complex due to the number of equations that form the boundary. Using colored pencils can help to figure out where the important region will exist.
(2, 1)
(6, 1)

6. For the next class:
Download and print a copy of Linear Programming on the Graphing Calculator Cheat Sheet from the class web site.