Question

The sum of the digits of a two-digit number is 9. If 9 is added to the number, the digits of the number are reversed. Write the equation for these statements.

Hint:

Define digits properly and form equations based on place values.

Answer 1

Let the two-digit number be \( 10x + y \), where \( x \) and \( y \) are its digits.
Given:
\[ x + y = 9. \] Also, when 9 is added, the digits reverse:
\[ 10x + y + 9 = 10y + x. \] Rearrange:
\[ 10x + y + 9 - x - 10y = 0. \] \[ 9x - 9y = -9. \] Dividing by 9:
\[ x - y = -1. \] Thus, the system of equations is:
\[ x + y = 9, \quad x - y = -1. \]