so i thought that the answer was D. if x=y then we have y^2-2y+1=1
which simplifies to y(y-2)=0 so y = 0 or y = 2.
since x=y we have:
(0-1)(0-1)=1 and (2-1)(2-1)=1.
what did i miss here?
You can not solve it the like this. From your equation, you solve it like you already assume (x-1)(y-1)=1, and of course the answer you get will be the one fit the criteria. You need to look at the ones doesn't fit as well. What about x=y=3? It does fit the description that xy>0, but in case of x=y=3 (x-1)(y-1) does not equal to 1. Therefore, insufficient.