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Math Help - How to solve this system of equations?

  1. #1
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    How to solve this system of equations?

    I have never solved any system consisting of squared numbers. I have been trying to figure this one out now for a while without any luck.

    x^2 - y^2 = -(15/4)
    2xy = 2

    Basically, what I would like to do is
    2xy = 2 <=> xy = 1 <=> x = 1 / y
    then insert that into the top equation, but doing so will give me a new grade four equation, which cannot be right?
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  2. #2
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    Quote Originally Posted by Sabo View Post
    I have never solved any system consisting of squared numbers. I have been trying to figure this one out now for a while without any luck.

    x^2 - y^2 = -(15/4)
    2xy = 2

    Basically, what I would like to do is
    2xy = 2 <=> xy = 1 <=> x = 1 / y
    then insert that into the top equation, but doing so will give me a new grade four equation, which cannot be right?
    \frac{1}{y^2} - y^2 = -\frac{15}{4}

    multiply every term by 4y^2 ...

    4 - 4y^4 = -15y^2

    0 = 4y^4 - 15y^2 - 4

    0 = (4y^2 + 1)(y^2 - 4)

    finish up.
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