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Find the solution set of the equation {x^2+y^2=34
{x+y=2

  • Math -

    Eq1: x^2 + y^2 = 34
    Eq2: x + y = 2

    x + y = 2
    Y = 2 - x

    In Eq1, replace Y with 2 - x.
    x^2 + (2-x)^2 = 34
    x^2 + 4 - 4x + x^2 = 34
    2x^2 -4x + 4 = 34
    2x^2 -4x - 30 = 0
    Divide both sides by 2:
    x^2 - 2 - 15 = 0
    (x+3)(x-5) = 0

    x+3 = 0
    X = -3.
    Y = 2- x = 2-(-3) = 5

    x-5 = 0
    X = 5.
    Y = 2 - 5 = -3.

    Solution sets: (-3,5),(5,-3).

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