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Thread: Finding substitution for simultaneous equation

  1. #1
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    Finding substitution for simultaneous equation

    Hi,

    I'm a bit stuck with trying to solve these simultaneous equations:

    k(k-m) =12
    k(k+m) = 60

    I'm familiar with the substitution process when one is clearly linear and the other a polynomial but both are polynomials here and I've tried to find m in terms of k but keep getting wrong answers. Help appreciated.
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  2. #2
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    Re: Finding substitution for simultaneous equation

    k-m = \frac{12}{k}

    k+m=\frac{60}{k}

    (k-m) + (k+m) = 2k = \frac{72}{k}

    k^2=36
    Last edited by abender; Sep 18th 2017 at 01:09 PM.
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  3. #3
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    Re: Finding substitution for simultaneous equation

    Double post.
    Last edited by abender; Sep 18th 2017 at 01:04 PM. Reason: Double Post
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  4. #4
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    Re: Finding substitution for simultaneous equation

    Not sure I follow that - I thought one would have to find m in terms of K so be able to isolate m ?
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  5. #5
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    Re: Finding substitution for simultaneous equation

    That makes sense to me now! Thanks!
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  6. #6
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    Re: Finding substitution for simultaneous equation

    Quote Originally Posted by Simonsky View Post
    I'm a bit stuck with trying to solve these simultaneous equations:
    $ \begin{align*}k(k-m) &=12 \\k(k+m) &= 60 \end{align*}$
    We can just add to get
    $2k^2=72$ or $k^2=36$ giving $k=\pm 6$.
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  7. #7
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    Re: Finding substitution for simultaneous equation

    Thanks -I got obsessed with isolating 'm' when it was quite easy to solve!
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  8. #8
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    Re: Finding substitution for simultaneous equation

    It's usually better to think in terms of eliminating a variable rather than isolating it.
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