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Math Help - [SOLVED] solving a system

  1. #1
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    [SOLVED] solving a system

    Can someone point me in the right direction to solve this system of equations?

    x^2 + y^2 = 25
    3x^2 - 16y = 0

    I'm trying to use substitution to get the answer. However, regardless of which direction I go, the answers get hopelessly convoluted. Can someone point me at how to start?
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  2. #2
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    Quote Originally Posted by satis View Post
    Can someone point me in the right direction to solve this system of equations?

    x^2 + y^2 = 25
    3x^2 - 16y = 0

    I'm trying to use substitution to get the answer. However, regardless of which direction I go, the answers get hopelessly convoluted. Can someone point me at how to start?
    x^2 = 25 - y^2

    3(25-y^2) - 16y = 0

    75 - 3y^2 - 16y = 0

    3y^2 + 16y - 75 = 0

    (3y+25)(y-3) = 0

    y = -\frac{25}{3}

    y = 3


    x^2 = 25 - \left(-\frac{25}{3}\right)^2 = -\frac{400}{9}<br />
    no solution for x in this equation. this y-value is invalid.

    x^2 = 25 - 9 = 16

    x = \pm 4

    so, two solutions ... (4,3) and (-4,3)
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  3. #3
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    excellent, thank you, that was precisely what I needed.
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