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Math Help - Simoultaneous equations

  1. #1
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    Simoultaneous equations

    Hey there,

    Getting very stuck on solving these, ive tried using substitution but i dont know how to rearrange it...
    can you help?

    137.9 = x + \frac{y}{\sqrt{0.05}}

    and

    275.8 = x + \frac{y}{\sqrt{0.007}}
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  2. #2
    Super Member Bacterius's Avatar
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    Hi,
    to rearrange for y in the first equation, you can substract x then multiply by \sqrt{0.05}. So you find :

    275.8 = x + \frac{\sqrt{0.05}(137.9 - x)}{\sqrt{0.007}}

    So :

    275.8 = x + \frac{\sqrt{0.05}}{\sqrt{0.007}} (137.9 - x)

    Setting a = \frac{\sqrt{0.05}}{\sqrt{0.007}} to make it a bit simpler, we are left with :

    275.8 = x + a (137.9 - x)

    So :

    275.8 = x + 137.9a - ax

    275.8 - 137.9a = x - ax

    275.8 - 137.9a = x(1 - a)

    \frac{275.8 - 137.9a}{1 - a} = x

    Substituting back the value we chose for a, we get :

    x = \frac{275.8 - 137.9 \left ( \frac{\sqrt{0.05}}{\sqrt{0.007}} \right )}{1 - \frac{\sqrt{0.05}}{\sqrt{0.007}}} \approx 55.454

    Finding the value of y is now straightforward

    Does it make sense ? Remember not to get stopped by impressive square roots and stuff : as long as there are no x terms in them, they can be considered a constant (and thus substituted to some letter, a in my example)
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  3. #3
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    ah yes that helps thanks very much!
    i see the way you got the unkown terms on one side, very nice

    Thanks again,

    Max
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  4. #4
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    Quote Originally Posted by darksupernova View Post
    Hey there,

    Getting very stuck on solving these, ive tried using substitution but i dont know how to rearrange it...
    can you help?

    137.9 = x + \frac{y}{\sqrt{0.05}}

    and

    275.8 = x + \frac{y}{\sqrt{0.007}}
    Since 275.8 is double 137.9, then you can go this simpler way:

    x + y/sqrt(.007) = 2x + 2y/sqrt(.05)
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  5. #5
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    Seeing "x" alone in both equations, the first thing I would think of is subtracting one equation from the other:
    275.8 = x + \frac{y}{\sqrt{0.007}}
    137.9 = x + \frac{y}{\sqrt{0.05}}

    137.9= \frac{y}{\sqrt{0.007}}- \frac{y}{\sqrt{0.05}}= y\left(\frac{1}{\sqrt{0.007}}- \frac{1}{\sqrt{0.05}}\right)

    137.9= y\left(\frac{\sqrt{0.05}- \sqrt{0.007}}{\sqrt{(0.05)(.007)}}\right)

    y= \frac{137.9\sqrt{0.00035}}{\sqrt{0.05}- \sqrt{0.007}}
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