Given that x and y are integers, then for the equation x+y= 2xy how many solutions are there?

Answer 1

2 x-1!=0, y = x/(2 x-1)

!= means doesn't equal.

Answer 2

so, since x and y are integers,

clearly x=y=0 is a solution

If x>0, 2x-1 > x unless x=1, so x=y=1 is a solution

For x>1, x/(2x-1) is a fraction.

For x<0, x/(2x-1) is always a fraction, so

(0,0) and (1,1) are the only integer solutions.