Linear Inequalities by Graphing

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Solving Systems of Inequalities by Graphing

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Presentation transcript:

Linear Inequalities by Graphing 6.6 – Solving Systems of Linear Inequalities by Graphing Definitions of the Day (DODs) System of Linear Inequalities Solution to a System of Linear Inequalites

Definition: System of Inequalities – Two or more inequalities solved together. (by graphing) Definition: Solution to a System of Inequalities – Any region that is common to all inequalities (makes all inequalities true)

Let’s Explore!! Test Points (0, 0) (0, 5) (3, 3) (1, 0) F F F T T T T F

Let’s Explore!! Test Points (-3, 0) (0, 0) (5, 0) T F T T F T

Solving Systems of Linear Inequalities by Graphing Steps: Carefully graph each inequality as if they were equations. 2. Carefully test a point in each region for all inequalities. Three possibilities: - 4 regions if lines intersect at a point - 3 regions if lines are parallel - 2 regions if the same line 3. Shade the region where all of the inequalities are true.

Example

Example

Your Turn!! Solve the following systems by graphing

Sentence Frames In a system of inequalities, you shade the region where ___________________________________________ ___________________________________________ There are three possibilities for the number of regions formed, They are: 1)__________________________________________ 2)__________________________________________ 3)__________________________________________