2011/007) the total number of integer pairs (x, y)

the total number of integer pairs (x, y) satisfying the equation x + y = xy is
a) 0
b) 1
c) 2
d) 3
None of these

we have x+y- xy = 0
subtract 1 from each side

x+y - xy - 1 = - 1
x(1-y) + (y-1) = -1

or (x-1)(1-y) = - 1
so x-1 = 1 and 1-y = -1 => x = 2 and y= 2

or x-1 = - 1 and 1- y = 1 => x= 0 and y =0

so 2 pairs