Question 2 of 4, Step 1 of 1

Find two positive numbers whose difference is 16 and whose product is 561 .

Answer
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Step 1 ：Set up a system of equations based on the given conditions. The first condition is that the difference between the two numbers is 16, which can be written as $x-y=16$. The second condition is that the product of the two numbers is 561, which can be written as $xy=561$.

Step 2 ：Solve this system of equations to find the values of x and y.

Step 3 ：The solution set includes two pairs of numbers, (-17, -33) and (33, 17). However, the problem specifies that we are looking for positive numbers. Therefore, the pair (-17, -33) is not a valid solution.

Step 4 ：The pair (33, 17) is the valid solution, where 33 and 17 are the two positive numbers whose difference is 16 and whose product is 561.

Step 5 ：The final answer is: The two positive numbers are $\boxed{{\displaystyle 33}}$ and $\boxed{{\displaystyle 17}}$.