Question

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

Answer 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.