Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method :
The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

Let the digit at Unit’s place be x and digit at ten’s place be y
Then,the number= 10y + x
Also, the number obtained by reversing the order of the digits = 10x + y
According to the given condition,
x + y = 9    ...(i)
And 9(10y + x) = 2(10x + y)
⇒ 90y + 9x = 20x + 2y
⇒ 11x - 88y = 0
⇒ x - 8y = 0    ...(ii)
Subtracting equation (ii) from equation (i), we get
       9y = 9

Substituting this value ofy in equation (i), we get

x + 1 = 9

⇒    x = 9 - 1 = 8
Hence, the required number
= 10y + x
= 10(1)+ 8
= 10 + 8 = 18.