If x and y are integers, is y an even integer?

(1) 2y – x = x² – y²

(2) x is an odd integer.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

此题答案A，请问怎么推导的？

谢谢！

y^2+2y=x^2+x

y^2+2y+1=x^2+x+1

(y+1)^2=x(x+1)+1 右边恒为奇,则y+1恒为奇,则y恒为偶