To find the original number we will need to form and solve a system of equations. To begin, let's define our variables. Let x represent the number in the tens place and let y represent the number in the ones place. Since we know that the sum of these two numbers is 11, we can write our first equation.
x+y=11
Now, let's find the second equation. When the digits are kept in their original places, the value of the unknown number can be written as the expression (10x+y). If we swap their positions, we get the expression (10y+x) and the value increases by 27. Let's write this difference as an algebraic equation.
(10y+x)-(10x+y)=27
Now that we have two equations, we can solve the system using the Substitution Method.
