5.3 Solving Systems of Equations Using Elimination

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5.3 Solving Systems of Equations Using Elimination

• Objective
• -- To solve systems of equations using the
  elimination method

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Elimination Method

• The elimination method requires that the same
  variable in both equations of the system have the
  same numerical coefficient but opposite signs
• This allows the equations to be added together to
  eliminate one of the variables
• After adding, you will solve for the remaining
  variable
• After finding the value of the variable, you will
  then substitute that value into one of the
  original equations to find the value of the
  second variable
• Some equations will require that you multiply
  them by a number to obtain variables with same
  numerical coefficients with opposite signs

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Example

• Solve
• Since the variable s has
• the same coefficient with
• opposite sign, add the
• equations.
  ------------------------
• Divide both sides by 2
• to get
  
• Substitute this back into one of the originals to
  find s
• 
  
• Subtract 98 from both sides
• Multiply by -1 to change signs
  So the solution is
  (f, s) (98, 65)
  
  

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Solve
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Solve
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Solve
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Solve
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Solve