Simultaneous Equations: Two-Digit Number Problem

The sum of the digits of a two-digit number is \(9\).

1. Letting the tens digit and the ones digit of the number be \(x\) and \(y\) respectively, form an equation to represent the above information.
   

When the digits of the number are reversed and the resulting number is subtracted from the original number, the result obtained is \(45\).

2. Form an equation to represent the above information, and show that the equation simplifies to \(x-y=5\).
   
3. Hence, find the original number by solving the pair of simultaneous equations from (a) and (b).