2.6 Solving Systems of Linear Inequalities

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Presentation transcript:

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.

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.

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