Question

Question 2 (iii)
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.

Answer 1

Let the unit digit and tens digits of the number be x and y respectively.
Then, the number will be $10y+x$
Number after reversing the digits is $10x+y$
According to the question,
$x+y=9...\left(i\right)$
$9(10y+x)=2(10x+y)$
$88y-11x=0$
$-x+8y=0...\left(ii\right)$
Adding equation (i) and (ii), we get
$9y=9$
$y=1...\left(iii\right)$
Putting the value in equation (i), we get
$x=8$
Hence, the number is $10y+x=10\times 1+8=18$