The line 2x+3y=1 intersects the curve x(x+y)=10 at A and B. Calculate the coordinates of A and B.

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  1. solve the first for y
    3y = 1-2x
    y = (1-2x)/3 , now sub that into the other equation

    x(x+(1-2x)/3) = 10
    x(3x+1-2x)/3 = 10
    x(x+1)) = 30
    x^2 + x - 30 = 0
    (x+6)(x-5) = 0
    x = -6 or x = 5

    if x = 5, y = (1-10)/3 = -3
    if x = -6 , y = (1 + 12)/3 = 13/3

    So A = (5,-3) and B is (-6, 13/3)

    (of course it doesn't matter who is called A or B)

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