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Math Help - Simultaneous Equation

  1. #1
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    Simultaneous Equation

    Hi, I have been given a homework by my teacher to solve the following equations. I have the answers for the question but all of my attempts at them have ended up in completely the wrong answers.
    The answers for the questions are x = -1, y = -3 OR x = 1, y = 3
    The equations are:
    y=3x
    2y^2-xy=15
    Probably very simple but I've hit a block and cant manage to work it out.
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  2. #2
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    Re: Simultaneous Equation

    Well, what have you tried? If you replace "y" in the second equation by "3x", you get a very simple quadratic equation in x alone. What quadratic equation and how do you solve it?
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  3. #3
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    Re: Simultaneous Equation

    I tried subbing 3x in as Y.
    Ended up something like:
    2(3x)(3x)-3x^2=15
    6x^2-3x^2=15
    6x^2-3x^2-15=0
    But I then dont know where to go from there, or if the answers are ever right.
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  4. #4
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    Re: Simultaneous Equation

    y = 3x

    2y^2 - xy = 15

    substitute 3x for y in the second equation ...

    2(3x)^2 - x(3x) = 15

    mind your order of operations ...

    18x^2 - 3x^2 = 15

    15x^2 - 15 = 0

    15(x^2-1) = 0

    15(x-1)(x+1) = 0

    finish it
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