A is the answer, correct?

prachich1987 wrote:If x^2 + y^2 =1, is x + y =1?
(1) xy =0
(2) y = 0

I am aware that the above question has been discussed earlier on the forum.
But I would like to know how to tackle with statement 2
Is it sufficient?

For many test-takers, the safest approach for this sort of question is to plug in values.

Many data sufficiency questions test the following differences:
Even vs. Odd
Positive vs. Negative
Integer vs. Fraction

We should bear these differences in mind as we choose values.

Statement 1: xy = 0.
Let x=1, y=0.
This combination works because xy = 1*0 = 0 and x²+y² = 1² + 0² = 1.
Does x+y = 1? Yes, because 1+0 = 1.

Let x=-1, y=0.
This combination works because xy =-1*0 = 0 and x²+y² = (-1)² + 0² = 1.
Does x+y = 1? No, because -1 + 0 = -1.
Since the answer can be both Yes and No, insufficient.

Statement 2: y = 0.
In each of the combinations used in statement 1 above, y=0.
Since one combination yields an answer of Yes and the other combination yields an answer of No, insufficient.

Statements 1 and 2:
The two combinations used above satisfy both statements.
Since one combination yields an answer of Yes and the other combination yields an answer of No, insufficient.

The correct answer is E.

Thank you for the explanations. Careless mistake on my part.