1. 2.6 Solving Systems of Linear Inequalities
Objectives: Graph systems of inequalities. Find the maximum or minimum value of a function defined for a polygonal convex set.

2. System of Linear Inequalities:
A set of inequalities with the same variables.
Ex. 1)
Solve the system of inequalities by graphing:
-x + 2y < 2
x < 4
Polygonal convex set:
A bounded set of all points on or inside a convex polygon graphed on a coordinate plane
Ex. 2)
Solve by graphing.
x > 0 , y > 0 , x + y < 5
Name the coordinates of the vertices of the polygonal convex set.

3. Ex. 3)
Evaluate f(x,y) = 3x + 2y – 4 for f(-3,5)
Vertex Theorem:
The maximum or minimum value of f(x,y)=ax + by + c on a polygonal convex set occurs at a vertex of the polygonal boundary.
Ex. 4)
Find the maximum or minimum values of
f(x)= y – 2x + 5 for the polygonal convex set determined by the system of inequalities.
x > 1 , y > 2 , y < 8 , x + y > 5 , 2x + y < 14