Definitions of the Day (DODs) 6.6 – Solving Systems of Linear Inequalities by Graphing System of...
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Transcript of Definitions of the Day (DODs) 6.6 – Solving Systems of Linear Inequalities by Graphing System of...
Definitions of the Day (DODs)
6.6 – Solving Systems of Linear Inequalities by Graphing
• 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!! Graph
3 1y x
Graph
3x y
Test Points(0, 0)(0, 5)(3, 3)(1, 0)
F FF TT TT F
Let’s Explore!! Graph
3 1y x
Graph
3 2y x Test Points
(-3, 0)(0, 0)(5, 0)
T FT TF T
Steps:1. 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.
Solving Systems of LinearInequalities by Graphing
Example3
22Graph:
12
2
y x
y x
Example4 4
Graph: 12
4
x y
y x
Your Turn!!
4
2
y
x
1. Solve the following systems by graphing
3 4
2 1
y x
y x
Sentence Frames
1. In a system of inequalities, you shade the region where ___________________________________________
___________________________________________
2. There are three possibilities for the number of regions formed, They are: 1)__________________________________________2)__________________________________________3)__________________________________________