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substitute the value of statement 1 in 2 or statement 2 in 1, we can cancel out y^2 and say that xy=x^2

Yeah, I know. I was showing you a way in which each statement by itself is sufficient. If my reasoning is correct then answer should be D instead of C. (D beats C in DS)

For statement 1: xy has to be + since yy is + and xy=yy so either x=y or -x=-y will work.

For statement 2: we agree that x=-1 and y=1 will work since xx & yy will be positive so it doesnt matter what the sign for x or y is but it will for the stem xy=xx

1) consider (1,0). It makes (1) correct, but it does not make the problem correct. (1,1) on the other hand, makes both of them correct. Insufficient.

2) tells us only that the absolute value of X is the absolute value of y. not sufficient, since if x is negative and y is positive, that the equation holds, but if x is positive and y is negative, the equation does not hold. insufficient.