Standard: Alg. 6.0

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U2-S3-L6 Systems of Inequalities

• Standard Alg. 6.0 9.0
• Objective Graph and solve systems of linear
  inequalities.
• Essential Question
• How do you solve and model systems of linear
  inequalities?

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Predictions

1. If you know how to graph one linear inequality,
   how do you think you will graph a system of
   linear inequalities?
2. If you know the solution to a linear inequality
   is a region that makes the inequality true, then
   what will the solution of a system look like?

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Vocabulary

• A system of linear inequalities is a set of two
  or more linear inequalities.
• The solution set is the set of all ordered pairs
  in the overlapping regions.

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Example 1 Identifying Solutions
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Example 2 Solving by Graphing

• To graph a system
• Put both equations in slope-intercept form
• Graph the first inequality
• Plot the y-intercept and use the slope
• Make a dashed or solid line
• Shade above or below the line
• Graph the second inequality
• Plot the y-intercept and use the slope
• Make a dashed or solid line
• Shade above or below the line
• The overlapping region they both share is the
  solution set. All the ordered pairs in this
  region are true.

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Example 2 Solving by Graphing
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Example 2 Practice
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Example 3 Parallel Lines

• Parallel lines will have NO SOLUTION only if the
  shaded area dont intersect.

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Example 3 Practice
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Example 4 Application

• 1)Write the system
• 2) Graph the system
• 3) Look at overlapping region to identify two
  possible combinations.

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REVIEW

• How can you check that you shaded the correct
  areas?
• How do you choose which region to select possible
  answers from?
• Do parallel lines of inequalities always have no
  solution? Why or why not?

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SUMMARY

• Answer the essential question in detailed,
  complete sentences.
• How do you solve and model systems of linear
  inequalities?
• Write 3-5 Study Questions in the left column to
  correspond to the notes.