3'3: Graphing and Solving Systems of Linear Inequalities

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3.3 Graphing and Solving Systems of Linear
Inequalities

• Intro Systems of inequalities are similar to
  systems of equations. A solution is still an
  ordered pair that is true in both statements.
• The graphing is a little more sophisticated -
  its all about the shading.

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Graphing Method

• Example Graph the inequalities on the same
  plane x y lt 6 and 2x - y gt 4.
• Before we graph them simultaneously, lets look
  at them separately.
• Graph of x y lt 6. ---gt

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Graphing Method

• This is 2x - y gt 4.

So what happens when we graph both inequalities
simultaneously?
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Coolness Discovered!

• Wow!
• The solution to the system is the brown region -
  where the two shaded areas coincide.
• The green region and red regions are outside the
  solution set.

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So what were the steps?

• Graph first inequality
• Shade lightly (or use colored pencils)
• Graph second inequality
• Shade lightly (or use colored pencils)
• Shade darkly over the common region of
  intersection.
• That is your solution!

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Challenge Extended

• Graph
• y -3x -1 and
• y lt x 2

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What about THREE inequalities?

• Graph x 0, y 0, and 4x 3y 24
• First off, lets look at x 0 and y 0
  separately.

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Graphing THREE inequalities

• Now lets look at x 0 and y 0 together.

Clearly, the solution set is the first quadrant.
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Graphing THREE inequalities

• So therefore, after we graph the third
  inequality, we know the solution region will be
  trapped inside the first quadrant. So lets look
  at 4x 3y 24 by itself.

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Graphing THREE inequalities

• Now we can put all of our knowledge together.
• The solution region is the right triangle in the
  first quadrant.