Simultaneous Equations

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Simultaneous Equations

• The Bare Bones

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Main Points

• Solve two (or more) equations at the same time
  (simultaneously)
• Only one set of numbers will satisfy (work in)
  both equations
• If you set out your working carefully you can
  collect most of the marks even if your answer is
  incorrect

3
Rough Guide to solving sim. Equations.

• Always number your equations - this makes it
  easier to show your working.
• Take your time - these will be worth a lot of
  marks.
• No short-cuts.

4
The Nuts and Bolts

• You must have either the same number of xs or
  ys. - if not you will need to multiply one or
  more equations.
• Find either x or y by adding or subtracting and
  then substitute that value into one of the
  equations to find the other value.
• Always check your answers in the remaining
  equation

5
Same Sign Subtract

• Solve 2x y 8
• and 5x y 17
• - 3x 0 9
• x 3
• Substitute x 3 in 2 x 3 y 8 so y
  2
• Check in (not used directly to find y)
• 5 x 3 2 17 so x 3 and y 2

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Different Signs Add

• Solve 3x 2y 8
• x - 2y 0
• 4x 0 8 so x 2
• Substitute x 2 in to find y
• 3 x 2 2y 8 so 2y 2 so y 1
• Check in 2 - 2 x 1 0
• So x 2 and y 1

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Different amounts of x and y

• Solve x 2y 11
• and 3x y 18
• Need either same number of xs or ys so x3
• This gives 3x 6y 33
• (SSS) - 0 5y 15 so y 3
• Sub y 3 in x 2x3 11 so x
  5
• Check in 3x5 3 18 so x 5 and y 3

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Fin

• The End