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Math Help - Real Solutions

  1. #1
    Member Rimas's Avatar
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    Real Solutions

    How many real solutions [x,y] are there that satisfy the two equations x^2 + y^2= 30 and 4y^2-X^2=100?
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  2. #2
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    You have a circle and hyperbola.
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  3. #3
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    Hello, Rimas!

    Did you try solving the system?


    How many real solutions (x,y) are there that satisfy: . \begin{array}{cc}(1)\\(2)\end{array}\;\begin{array  }{cc}x^2 + y^2\:=\:30 \\ 4y^2-x^2\:=\:100\end{array}

    Add the equations: . 5y^2 = 130\quad\Rightarrow\quad y^2 = 26\quad\Rightarrow\quad y = \pm\sqrt{26}

    Substitute into (1): . x^2 + 26 \:=\:30\quad\Rightarrow\quad x^2 = 4\quad\Rightarrow\quad x = \pm2


    There are four solutions: . (2,\,\sqrt{26}),\;(2,\,\text{-}\sqrt{26}),\;(\text{-}2,\,\sqrt{26}),\;(\text{-}2,\,\text{-}\sqrt{26})

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