Find all ordered pairs (x, y) satisfying x + y = 9 and xy = 14.
Note
Here x and y are two numbers whose sum is 9 and product is 14. A useful HSC-level trick is to think of them as roots of the quadratic equation t² - (9)t + (14) = 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 9 and product 14. Therefore the correct answer choices are (7, 2), (2, 7).
