One number is 4 more than 2 times another. Their product is 4 more than 2 times their sum. Find the numbers

Question

I cannot figure this out for the life of me, thought I had y=3, -2 which would give me x=0, 13 which would give me (0,-2) or (13/3)

Answer 1

x= 4 + 2y

xy = 4+ 2(x+y) = 4+ 2x + 2y

xy = 4 + 2x + 2y

(4+2y)y = 4 + 2(4+2y) + 2y

4y + 2y^2 = 4 + 8 + 4y + 2y

2y^2 -2y -12 = 0

y^2 - y - 6 = 0

(y-3)(y+2) = 0

y = -2, 3

x = 4+ 2(-2) or 4 + 2(3) = 0 or 10