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Math Help - [SOLVED] Simultaneous equation

  1. #1
    vincenzo
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    [SOLVED] Simultaneous equation

    Solve the pair of simultaneous equations.

    4e + 5f = 86
    2f - e = 11
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  2. #2
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    earboth's Avatar
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    Quote Originally Posted by vincenzo View Post
    Solve the pair of simultaneous equations.

    4e + 5f = 86
    2f - e = 11
    Hello,

    there are a lot of different methods to solve this system of simultaneous equations. I'll demonstrate 2 of them:

    First rearrange the 2nd equation!


    1. \left| \begin{array}{lcr}4e+5f&=&86\\-e+2f&=&11\end{array}\right. multiply the 2nd equation by 4: \left| \begin{array}{lcr}4e+5f&=&86\\-4e+8fe&=&44\end{array}\right. and add columnwise:

    13f=130~\iff~f=10 . Plug in this result into any of the 2 equations and solve for e. \left(e=9\right)

    2. Solve the 2nd equation for e: e = 2f - 11 and substitute e by this term in the first equation:

    4(2f-11)+5f=86~\iff~13f=130

    Plug in the result for f into the 2nd equation.
    Last edited by earboth; January 2nd 2008 at 03:53 AM.
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