Find all ordered pairs (x, y) satisfying x + y = 4 and xy = 3.
Note
Here x and y are two numbers whose sum is 4 and product is 3. A useful HSC-level trick is to think of them as roots of the quadratic equation t² - (4)t + (3) = 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 4 and product 3. Therefore the correct answer choices are (1, 3), (3, 1).
