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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.

The sum of two numbers is negative thirteen, and one number is nine less than the other. Using the variables m and n to represent the two numbers, write a system of equations that describe the situation. Find the two numbers.

This problem involves solving a system of linear equations where the sum of two numbers is -13, and one number is 9 less than the other. Learn how to use algebraic techniques like substitution to find the solution.

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