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Math Help - I'm struggling to solve this strange simultaneous equation. Can someone help me?

  1. #1
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    Lightbulb I'm struggling to solve this strange simultaneous equation. Can someone help me?

    Solve the pair of simultaneous equations:
    x+y=2xy
    x-y=xy

    I solved it to get x=2 and y=0.66
    but the answer booklet says it is wrong?
    can someone please explain
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: I'm struggling to solve this strange simultaneous equation. Can someone help me?

    I get (x,y) = (2,2/3) or (0,0). What does your booklet gives as the solution?
    Last edited by MarkFL; September 13th 2012 at 06:43 AM.
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  3. #3
    Junior Member BobBali's Avatar
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    Re: I'm struggling to solve this strange simultaneous equation. Can someone help me?

    You have two equations: 1) x+y = 2xy 2) x-y =xy

    In the first equation make y the subject. This gives you your third equation 3) y = 2xy-x > simplify > y = x(2y-1)

    Sustitute this 3rd equation into the 2nd equation and solve it simultaneously.

    I get x = 2x(2y-1) and y = -2x(y-1) Hope this helps! :-)
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  4. #4
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    Re: I'm struggling to solve this strange simultaneous equation. Can someone help me?

    Quote Originally Posted by BobBali View Post
    You have two equations: 1) x+y = 2xy 2) x-y =xy
    In the first equation make y the subject. This gives you your third equation 3) y = 2xy-x > simplify > y = x(2y-1)
    Sustitute this 3rd equation into the 2nd equation and solve it simultaneously.
    I get x = 2x(2y-1) and y = -2x(y-1) Hope this helps! :-)
    Keep it simple:
    x+y=2xy
    x-y=xy
    Simply add the equations together: 2x = 3xy ; 2 = 3y ; y = 2/3
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  5. #5
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    Re: I'm struggling to solve this strange simultaneous equation. Can someone help me?

    Quote Originally Posted by MarkFL2 View Post
    I get (x,y) = (2,2/3) or (0,0). What does your booklet gives as the solution?
    Sorry guys there was a mistake in the answer booklet.
    x=2
    y=0.66 is correct
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