Solving By Elimination Method

Let the ten's and the unit's digits in the first number be $x$ and $y$, respectively, so the number is $10x + y$. When the digits are reversed, the number becomes $10y + x$. According to the problem, the sum of these numbers is 66, which gives the equation $(10x + y) + (10y + x) = 66$. Simplifying this equation by combining terms to get $11(x + y) = 66$ and dividing by 11 yields the first linear equation: . We are also given that the digits differ by 2, which gives us the second equation $x - y = 2$ (assuming $x > y$). By applying the elimination method and adding the two simplified equations together, we eliminate $y$ to get $2x = 8$, which means $x =$ . Substituting this value back into the first equation, we find that $y =$ , giving us the final two-digit number 42.