Final answer:
The two numbers that have a sum of 69 and a difference of 1 are 35 and 34. We used a system of two equations to solve for these numbers.
Step-by-step explanation:
To find two numbers whose sum is 69 and whose difference is 1, we can set up two equations based on the problem statements: (1) x + y = 69 (sum of two numbers) and (2) x - y = 1 (difference of two numbers). To solve the system of equations, you can add both equations together to eliminate the y variable.
Adding (1) and (2), we get 2x = 70. Dividing by 2 gives us x = 35. Now, you can substitute x back into either (1) or (2) to find y. Using equation (1): 35 + y = 69. Subtracting 35 from both sides yields y = 34.
Therefore, the two numbers we are looking for are 35 and 34. Their sum is 35 + 34 = 69, and their difference is 35 - 34 = 1, which satisfies both conditions of the problem.