Let the two natural numbers be $x$ and $y$.

From the problem:

• The two numbers add up to 25: $x + y = 25$
• One number is 9 more than the other: $x = y + 9$

Now, we can substitute the second equation into the first: $(y + 9) + y = 25$ Simplifying: $2y + 9 = 25$ Subtract 9 from both sides: $2y = 16$ Divide by 2: $y = 8$

Now, substitute $y = 8$ back into the second equation to find $x$: $x = 8 + 9 = 17$

Thus, the two numbers are $x = 17$ and $y = 8$.

Final result:

The two numbers are 17 and 8.

Would you like more details on the process or any other questions?

Here are some related questions:

1. What if the difference between the two numbers were 7 instead of 9?
2. Can you solve for two numbers that sum up to 30 with the same conditions?
3. How would this change if the two numbers were consecutive?
4. Can you solve for the numbers if their product was given instead of the sum?
5. What if one number is double the other, and their sum is still 25?

Tip: When solving systems of equations, substitution or elimination methods are very effective for finding solutions quickly!