The problem provides two conditions involving two unknown numbers, $m$ and $n$. Let's break it down:

Conditions:

1. The sum of the two numbers is $-13$: $m + n = -13$
2. One number is 9 less than the other: $m = n - 9$

System of Equations:

The system of equations based on the given conditions is: $m + n = -13, \quad m = n - 9$

Solving the system:

1. Substitute the second equation $m = n - 9$ into the first equation $m + n = -13$: $(n - 9) + n = -13$
2. Simplify and solve for $n$: $2n - 9 = -13$ $2n = -13 + 9$ $2n = -4$ $n = -2$
3. Substitute $n = -2$ into $m = n - 9$: $m = -2 - 9 = -11$

Final answer:

The two numbers are $m = -11$ and $n = -2$.

Would you like more details or have any questions?

Here are 5 related questions for further practice:

1. What if the sum of the numbers was positive? How would the solution change?
2. How can you verify the solution for $m + n = -13$ and $m = n - 9$?
3. What happens if the second condition was $m = n + 9$?
4. Can you solve this system graphically by plotting the two equations?
5. How would the approach change if the difference between the numbers was different, say $7$ instead of $9$?

Tip: Always double-check your solution by substituting the values back into the original conditions.