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The point (x,y) lies on both conics x2+xy+x=81 and y2+xy+y=51. Given that x+y is positive, determine the value of x+y.

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    x^2 + xy + x = 81
    xy + y^2 + y = 51

    add them to get

    x^2 + 2xy + y^2 + x + y = 132
    (x+y)^2 + (x+y) - 132 = 0
    ((x+y)+13)((x+y)-12) = 0
    so, x+y = 12

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