a two digit number is four times the sum of its digits and twice the product of the digit. find the number using elimination method

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  1. let the tens digit be x
    let the unit digit be y

    then the number is 10x+y

    10x+y = 4(x+y) ----> 6x - 3y = 0
    6x = 3y
    y = 2x

    10x + y = 2(xy)
    10x - 2xy + y = 0
    10x - 2x(2x) + 2x = 0
    -4x^2 + 12x = 0
    x^2 - 3x= 0
    x(x-3) = 0
    x = 0 or x = 3 , but if x=0 you don't have a 2-digit number

    x = 3, y = 6
    the number is 36

    I used substitution instead of elimination since it was clearly the easiest and most obvious way to do it, because of the simple result of x=2x from the first equation.
    the xy term of the second equation would lead to a more complicated result using elimination.

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