If x ≠ y, what is the value of x + y?

(1) x - y = 1
(2) x^2- y^2 = x - y

Correct Answer is "B - Statement (2) ALONE is sufficient, but statement (1) is NOT sufficient"

But I believe it should be "D - EACH statement ALONE is sufficient". Why because:

Consider (2)

\(X2- y 2 = x - y\) => \((x+y)(x-y) = (x-y)\) => \(x+y = 1\) by cancelling \(x-y\) on both sides Sufficient

Now, consider (1) \(x - y = 1\).

Adding \(2y\) on both sides,

\(x+y = 1 + 2y.\)

I agree, this does not give a concrete answer like case 2 (which gave x+y = 1). But this expression "\(x+y = 1 + 2y\)" will help me find the answer for x+y provided I know the value of y. Isn't it?

The guide says,



Thus, I say I can find the value of x+y either with 1st 2nd statement alone (i.e., EACH statement ALONE is sufficient).

I am not saying I am correct. I know I am wrong because my answer is not matching with the correct answer. Its just that I do not seem to understand. Can someone correct me, please?