Form the pair of linear equations in the following problem and find their solution (if they exist) by any algebraic method:
The sum of the digits of a two-digit number is . Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
Step 1: Form the linear equations
Let us assume that the unit digit and tens digit of a number be and respectively.
Then, Number .
after reversing the order of the digits .
According to the given information,
Step 2: Find the solution
Adding the equations and we get,
Substituting this value of , in the equation we get
The number
Hence, the number is .