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Math Help - Simultaneous linear equations

  1. #1
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    Simultaneous linear equations

    Please help me solve the following by substitution:

    2y - x = 7

    y + 2x = 1

    After trying over and over i now know x=-1 and y = 3 but cant prove the math to show working, sort of stumbled on it
    ive gone over it time and time again but im baffled

    many thanks
    Last edited by Parton-Bill; November 17th 2008 at 09:34 AM. Reason: found results
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  2. #2
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    2Y - X = 7 equation 1
    Y + 2X = 1 equation 2

    Mutiply the second equation by 2 to get:

    2Y + 4X = 2

    Minus this new equation from the first equation:

    (2Y - X = 7) - (2Y +4X = 2)

    The ys cancel out leaving you with:

    -5x = 5
    so x= 1

    subsitute this back into thte second equation:
    y + 2 = 1
    y = -1

    hope this helps
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  3. #3
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    Please ignore me if im making an idiot out of myself here, but i see how those results relate to equation 2, but not to equation 1, i;m very new to this type of math so im still learnering the rules of it to a large extent.

    many thanks for your help by the way
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  4. #4
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    sorry thats my fault. Let me try again.

    The ys cancel out leaving you with:

    -5x = 5
    so x= -1

    subsitute this back into the second equation:
    y - 2 = 1
    y = 3

    to check we can substitute this into equation 1:

    2(3) - (-1) = 7
    6 + 1 = 7

    hope this helps again
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  5. #5
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    Now it all makes sense ha ha thank you William, very much appreciated
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  6. #6
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    ah problem, the method used appears to be the method of equating co-efficients, i need to use the solution by substitution
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  7. #7
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    Updated!!!

    How does this look?

    Equation 1 - 2y - x = 7

    Equation 2 - y + 2x = 1

    E1) x = 7 - 2y

    E2) y + 2(7 - 2y) = 1
    E2) y + 14 - 4y = 1
    E2) 14 - 5y = 1
    E2) 5y = 14 +1
    E2) 5y = 15
    E2) 15/5 = 3
    y = 3

    Substitute in E1

    2y - x = 7
    6 - x = 7
    6 - 7 = x
    x = -1

    Equation 1 = 2y - x = 7

    2 x 3 - (-1) = 7
    6 - (-1) = 7

    Equation 2 = y + 2x = 1

    3 + (2 x -1) = 1
    3 -(-2) = 1

    ???
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