Final answer:
To find the two numbers whose sum is 65 and the difference is 9, set up a system of equations: x + y = 65 and x - y = 9. Solve the system and find that x = 37 and y = 28.
Step-by-step explanation:
To find the two numbers whose sum is 65 and the difference is 9, we can set up a system of equations. Let x and y be the two numbers.
We have the equation x + y = 65 (the sum) and x - y = 9 (the difference).
To solve this system, we can add the two equations, which eliminates y. Therefore, 2x = 74. Divide both sides by 2 to find x = 37. Substituting x = 37 into one of the equations, we find y = 28.