# Chapter 4 Section 4.6 Solving Systems of Linear Inequalities.

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Chapter 4 Section 4.6 Solving Systems of Linear Inequalities

Systems of Inequalities A system of linear inequalities are several of linear inequalities all graphed on the same graph. The region where they all overlap is called the solution to the system. To solve the system of inequalities above we do the following: 1.Graph each inequality putting arrows on the correct side of the line instead of shading. 2.Shade in the region they will all overlap. 3.Located the points where the lines cross by using either substitution or elimination methods for intersecting lines (if required)

Sometimes more than two inequalities will need to be graphed on the same graph. If you are careful enough about how you graph the lines you can read come of the crossing points right off the graph.

-6-5-4-3-2123456 -6 -5 -4 -3 -2 1 2 3 4 5 6 To solve the system of inequalities above we do the following: 1. Graph each inequality putting arrows on the correct side of the line instead of shading. 2. Shade in the region they will all overlap. 3. Located the points where the lines cross by using either substitution or elimination methods for intersecting lines y = 0 x = 0 y = 4 y =-2 x +6 Solve the inequality y < -2 x +6 A B C D Point A is (0,0) Point B is (0,4) Point C is (3,0) Point D is (1,4) To find Point C To find Point D The points A, B, C and D are called Corner Points.

123456 1 2 3 4 5 6 Very often it is practical to have x and y not be negative and you get the inequalities x >0 and y >0 in the system of inequalities. Find the solution to the system below. x = 0 y = 0 Solve (0,0) (0,5)

123456 1 2 3 4 5 6 7 8 9 10 11 12 Solve: x =0 y =0 x =4