Find all ordered pairs (x, y) satisfying x + y = -7 and xy = 10.
Note
Here x and y are two numbers whose sum is -7 and product is 10. A useful HSC-level trick is to think of them as roots of the quadratic equation t² - (-7)t + (10) = 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 -7 and product 10. Therefore the correct answer choices are (-2, -5), (-5, -2).
