The sum of a two-digit number and the number obtained by reversing the digits is 88. If the digits of the number differ by 2, find the number. How many such numbers are there?

Let the ten’s and the unit’s digits in the first number be x and y, respectively.

So, the first number = 10x + y

After the digits have been reversed, the second number will be = x + 10y

As per the given statement;

(10x + y)+(10y + x) = 88

11x + 11y = 88

11(x + y) = 88

x + y = 8 ……….(1)

Also given, the difference between the two digits is equal to 2. Therefore;

x – y = 2 ………..(2)

or

y – x = 2 …………(3)

If we consider equation 1 and 2, then by elimination method we get,

x = 5  and y = 3

Hence, the number is 53.

If we consider equation 1 and 3, then by elimination method we get,

x = 3  and y = 5

Hence, the number is 35.

Therefore, there are two such numbers, 53 and 35.

Note: The elimination method is preferred over the substitution method when it is easy to multiply the coefficient and add or subtract the equations to eliminate one of the variables. The final aim is to form a linear equation in one variable so that it can be solved easily.