Find all ordered pairs (x, y) satisfying x + y = 0 and xy = -9.
Note
Here x and y are two numbers whose sum is 0 and product is -9. A useful HSC-level trick is to think of them as roots of the quadratic equation t² - (0)t + (-9) = 0. After factoring or solving that quadratic, we get the two possible numbers. Since the question asks for ordered pairs, the order matters: if the two numbers are different, both (first, second) and (second, first) are valid. Checking the selected pair(s), each one has sum 0 and product -9. Therefore the correct answer choices are (-3, 3), (3, -3).
