3'3 Graphing and Solving Systems of Linear Inequalities

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3.3 Graphing and Solving Systems of Linear
Inequalities

• Goal
• Graph a system of linear inequalities to find the
  solutions of the system

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System of Linear Inequalities

• Set of two or more linear inequalities with the
  same variables.
• lt or gt use a dashed line with values along
  the line not included
• ? or ? use a solid line with values
  along the line included

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Solving Systems of Linear Inequalities

• Example 1 Solving Systems of Linear Inequalities
• y -2x 4
• y gt x -3
• Graph the lines
• Shade the appropriate
• regions
• The overlapping shaded
• area contains the
• solutions

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Graph the System of Inequalities

• y 4
• 2x y lt 1

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Graph the System of Inequalities

• x ? 0
• y ? 0
• 4x 3y ? 24

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Graph the System of Inequalities

• y lt 5
• y gt -6
• 2x y ? -1
• y ? x 3

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Writing and Using a System of Inequalities

• 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 the person strive for a heart rate that is
  at least 70 of the maximum and at most 85 of
  the maximum.
• You are making a poster for health class. Write
  and graph a system of linear inequalities that
  describes the information given above.
• A 40-year old person has a heart rate of 150
  (heartbeats per minute) when exercising. Is the
  persons heart rate the target zone?

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Inequalities

• x ? 20
• x ? 65
• y ? 0.7(220 x)
• y ? 0.85(220 x)

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Homework

• Pg. 159 12 48 every 3rd Problem