Topic: Solving Systems of Equations by Substitution

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Topic Solving Systems of Equations by
Substitution

• X Y 5
• X Y -7

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Step One

• To solve the system by substitution method
• X Y 5
• X Y -7
• Solve one of the equations for X or Y. (It
  doesnt matter which one you choose. Pick the
  variable you think is easiest!)
• If X Y -7
• then X Y 7 ( just add y to both sides)

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Step Two

• X Y 5
• X Y -7 so X Y 7
• Substitute the value for X in for the X in the
  second equation.
• X Y 7 so in the equation X Y 5 when you
  substitute Y 7 in for X you get the equation (Y
  7) Y 5.

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Step Three

• Solve the equation for Y.
• ( Y 7 ) Y 5
• 2Y 7 5 (combine like terms)
• 2Y 12 (add 7 to both sides)
• Y 6 (divide both sides by 2)

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Step Four

• Use the solution for Y to find the answer for X
  using substitution again. (You may use either
  equation for the last substitution.)
• Remember Y 6
• If X Y 7, then using substitution
• X 6 7 and so X -1
• The solution to the system is (-1,6)

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Summary

• Solving by Substitution Method
• Sample X Y 5
• X Y -7
• X Y 7 ( Solve for X in the
  2nd equation)
• (Y 7) Y 5 (Substitute into the
  1st equation)
• 2Y 7 5 (Solve)
• 2Y 12
• Y 6
• so X 6 7
• and X -1.
• Solution to the system is (-1,6)

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If one of the equations in a system is already
solved for X or Y then it is born for the
Substitution Method!!

• If 4X 3Y 12 and Y 2X 5 then
• 2X 5 would be substituted for Y in the
  first equation.
• 4X 3(2x 5) 12
• 4X 6X 15 12
• 10X 15 12
• 10X 27
• X 2.7
• So if X 2.7 then Y 2(2.7) 5
• Y .4 and the solution to the system is (2.7,
  -.4)