6.6

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6.6 Solving Systems of Linear Inequalities by
Graphing

• System of Linear Inequalities
• Solution to a System
• of Linear Inequalites

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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)
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Lets Explore!!
Test Points (0, 0) (0, 5) (3, 3) (1, 0)
F F
F T
T T
T F
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Lets Explore!!
Test Points (-3, 0) (0, 0) (5, 0)
T F
T T
F T
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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.

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Example
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Example
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Your Turn!!

1. Solve the following systems by graphing

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• 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)__________________________________________