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Math Help - Simultaneous non-linear equations.

  1. #1
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    Simultaneous non-linear equations.

    {5xy(x + y) = -160
    {x + 5xy +y = -12
    ???
    Last edited by mr fantastic; September 19th 2011 at 07:28 PM. Reason: Re-titled.
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: No idea

    What do you have to do? Solve the system? ...
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  3. #3
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    Re: No idea

    Yes
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  4. #4
    MHF Contributor Siron's Avatar
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    Re: No idea

    The first thing I noticed is that you recognize two equal parts in both equations, the 5xy part and x^2+y^2

    So you can 'simplify' the system by saying, let x^2+y^2=a and 5xy=b therefore you get the two simultaneous equations:
    b\cdot a=-160 (1)
    a+b=-12 (2)

    Solve this system and afterwards do the back-substitution.
    Last edited by Siron; September 19th 2011 at 11:23 AM.
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  5. #5
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    Re: No idea

    Thank you very much
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  6. #6
    MHF Contributor Siron's Avatar
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    Re: No idea

    You're welcome!

    I'll give you a part of the solution,
    Solving the system by reforming (1) to b and substituting this in (2):
    a-\frac{160}{a}=-12
    \Leftrightarrow a^2-160=-12a
    \Leftrightarrow a^2+12a-160=0
    Two solutions: a=8 or a=-20
    But we have to reject a=-20 because a=x^2+y^2 is always >0.
    If a=8 then b=-20

    So now you can do the back-substitution and solve it.
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