Warm

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Warm up

• Toya is training for a triathlon and wants to
  bike and run on the same day. She has less than
  3 hours to spend on her workouts.
• What inequality represents the time Toya has to
  bike and run?
• What is the graph of the solutions?

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Answer

• b r lt 3

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Questions over hw?
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CCGPS Coordinate AlgebraDay 23 (9-13-12)
UNIT QUESTION How do I justify and solve the
solution to a system of equations or
inequalities? Standard MCC9-12.A.REI.1, 3, 5, 6,
and 12 Todays Question How do I find the
solutions to a system of linear inequalities
graphically? Standard MCC9-12.A.REI.12
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Solving Systems of Linear Inequalities in two
variables

• Coordinate Plane

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System of Inequalities

• Two or more inequalities in the same variables
  that work together

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Solution to a System of Linear Inequalities

• The intersection of the half planes of the
  inequalities.
• Look for the area where the shading overlaps.
  This is the solution.

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Steps for Graphing Inequalities

• Graph the lines and appropriate shading for each
  inequality on the same coordinate plane.
• Be sure to pay attention to whether the lines are
  dotted or solid.
• The solution is the section where all the
  shadings overlap.
• ?Sometimes it helps to use different color
  pencils for each line and shaded region. It
  makes it easier to determine the overlapped
  shaded regions.

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Ex.1
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Ex. 2
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Ex. 3

• It takes 2 hours to make the blade of a figure
  skate. It takes 3 hours to make the blade of a
  hockey skate. There is a maximum of 40 hours per
  week in which the blades can be made for both
  types of skates.
• It takes 3 hours to make the boot of a figure
  skate. It takes 1 hour to make the boot for a
  hockey skate. There is a maximum of 20 hours per
  week in which boots can be made for both types of
  skates.

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Ex. 3

1. What is the inequality that represents the time
   it takes to make the blades of the two different
   types of skates?
2. What is the inequality that represents the amount
   of time it takes to make the boots of the two
   different skates?

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Ex. 3

• Graph and consider some constraints to the
  problem.
• What is the solution of all possible combinations
  of figure skates and hockey skates that can be
  produced given the constraints of this situation?

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Ex. 3s Solution with constraints
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Ex. 4

• Which system of inequalities represents the graph
  below?

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Ex. 5
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Homework

• Worksheet