I don't understand this question (or the answers provided). Can anyone help me? Thanks!

If |x| + |y| = -x – y and xy does not equal 0, which of the following must be true?

The |x| + |y| on the left side of the equation will always add the positive value of x to the positive value of y, yielding a positive value. Therefore, the -x and the -y on the right side of the equation must also each yield a positive value. The only way for -x and -y to each yield positive values is if both x and y are negative.

(A) FALSE: For x + y to be greater than zero, either x or y has to be positive.

(B) TRUE: Since x has to be negative and y has to be negative, the sum of x and y will always be negative.

(C) UNCERTAIN: All that is certain is that x and y have to be negative. Since x can have a larger magnitude than y and vice-versa, x – y could be greater than zero.

(D) UNCERTAIN: All that is certain is that x and y have to be negative. Since x can have a larger magnitude than y and vice versa, x – y could be less than zero.

(E) UNCERTAIN: As with choices (C) and (D), we have no idea about the magnitude of x and y. Therefore, x2 – y2 could be either positive or negative.

Another option to solve this problem is to systematically test numbers. With values for x and y that satisfy the original equation, observe that both x and y have to be negative. If
x = -4 and y = -2, we can eliminate choices (A) and (C). Then, we might choose numbers such that y has a greater magnitude than x, such as x = -2 and y = -4. With these values, we can eliminate choices (D) and (E).

The correct answer is B.

hi -

could you please post the actual answer choices?
you've got the explanations for those choices, showing why they're true/false/undecided, but the stuff you've copied and pasted (or typed out) doesn't include the actual answer choices themselves.

thanks.