Question

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

$According \: to \: first \: condition$

$x + y = 9$

$According \: to \: second \: condition$

$9x - 2y = 9$

$Therefore, \: multiply \: 1st \: condition \: by \: 2$

$we \: get \: .$

$2x + 2y = 18$

$now \: add \: this \: equation$

$9x - 2y = 9$

$+$

$2x + 2y = 18$

$=$

$11x = 27$

$x = \frac{27}{11}$

$substituting \: x = \frac{27}{11}$

$\frac{27}{11} + y = 9$

$y = 9 - \frac{27}{11}$

$y = \frac{99 - 27}{11}$

$y = \frac{72}{11}$