By writing and solving a system of equations we will find that the number is 56
So we can write a two-digit number as:
a*10 + b
Where the two digits are a and b.
Here we must have:
a + b = 11
The reversed number is:
b*10 + a
Then we can write the equation:
b*10 + a - a*10 - b = 9
b*9 - a*9 = 9
Then we have a system of two equations:
a + b = 11
b*9 - a*9 = 9
We can divide both sides of the second equation by 9 to get:
b - a = 1
Now we can isolate b to get:
b = 1 + a
Now we can replace this in the other equation.
a + b = a + (1 + a) = 11
2a + 1 = 11
2a = 11 - 1 = 10
a = 10/2 = 5
Now we have the value of a, and we know that:
b = 1 + a = 1 + 5 = 6
Then the two-digit number is:
a*10 + b = 5*10 + 6 = 56
If you want to learn more about systems of equations, you can read:
https://brainly.com/question/13729904
