Find all ordered pairs (x, y) satisfying x + y = -5 and xy = 4.
Note
Here x and y are two numbers whose sum is -5 and product is 4. A useful HSC-level trick is to think of them as roots of the quadratic equation t² - (-5)t + (4) = 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 -5 and product 4. Therefore the correct answer choices are (-1, -4), (-4, -1).
