**Problem Statement:**
We need to find a two-digit number where the sum of its digits is 9. If we subtract 9 from the number, the digits are reversed.

**Solution:**
To solve this problem, we can use algebraic equations to represent the given conditions and find the required number.

Let's assume the tens digit of the number is 'x' and the units digit is 'y'. Therefore, the number can be represented as 10x + y.

**Condition 1: The sum of its digits is 9**
According to the given condition, the sum of the digits is 9. We can write this as an equation:
x + y = 9

**Condition 2: If 9 is subtracted from the number, the digits are reversed**
If we subtract 9 from the number, the digits are reversed. In other words, the new number with reversed digits can be represented as 10y + x. We can write this as another equation:
10x + y - 9 = 10y + x

Now, we have a system of two equations:
x + y = 9 (Equation 1)
10x + y - 9 = 10y + x (Equation 2)

**Solving the system of equations:**
We can solve this system of equations by substitution or elimination method to find the values of x and y.

Using the elimination method, we can subtract equation 1 from equation 2:
(10x + y - 9) - (x + y) = (10y + x) - (x + y)
9x - 9 = 9y - x
10x - x - 9 = 9y - y
9x - 9 = 8y
9x = 8y + 9 (Equation 3)

Now, we have two equations:
x + y = 9 (Equation 1)
9x = 8y + 9 (Equation 3)

**Solving Equation 3 for x:**
We can rearrange equation 3 to isolate x:
9x - 8y = 9
9x = 8y + 9
x = (8y + 9)/9

**Finding the possible values of x and y:**
Since the number is a two-digit number, both x and y should be integers between 0 and 9.

We can substitute the possible values of y (0 to 9) into equation 1 to find the corresponding values of x.

By substituting the values of x and y back into the equation 10x + y, we can find the two-digit number that satisfies the given conditions.

For example, if we assume y = 2, we can find x using equation 1:
x + 2 = 9
x = 9 - 2
x = 7

Therefore, the number is 10x + y = 10(7) + 2 = 72.

We can repeat this process for all possible values of y (0 to 9) to find the corresponding two-digit numbers that satisfy the given conditions.

Thus, we can find the required number by solving the system of equations and substituting the values back into the equation for the number.

They gave mate :)