Algebra II Lesson 3.3

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Algebra IILesson 3.3

• Graphing and Solving
• Systems of Linear Inequalities

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Systems of Linear Inequalities

• Sorry, we are back to graphing a little bit.
• The following is a system of linear inequalities.
• x y 6
• 2x y gt 4
• A solution to a system of linear inequalities is
  an ordered pair that is a solution to each
  inequality. Ex (3, -1) is a solution
• The graph of a system of linear inequalities
  shows all solutions.

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Investigating Graphs of Inequalities
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Graphing Systems of Linear Inequalities

• This is no harder than doing one graph of an
  inequality, you just do more than one on the same
  plane.

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Graphing Systems

• Graph the system
• y -3x - 1
• y lt x 2

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Solving a System of Three Inequalities Graphically

• Solve the system
• x 0
• y 0
• 4x 3y 12

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Writing and Using a System of Inequalties

• A persons theoretical maximum heart rate is 220
  x where x is the persons age in years 20 x
  65. When a person exercises, it is recommended
  that they stay at a minimum of 70 of max and a
  maximum of 85 of max. Write and graph a system
  of linear inequalities.
• A 40 yr old has a heart rate of 150. Is he in the
  target zone?

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Solution

• x 20
• x 65
• y 0.7(220 x)
• y 0.85(220 x)
• 40 yr old at 150bpm in zone?
• Yes at 40 the zone is 126 y 153

180
160
(40, 153)
140
120
(40, 126)
100
20
30
40
50
60
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Solution
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Questions GP 1 3, 7, 10, 11HW 12 24(3rd),
27 51(6th)