Question

Form the pair of linear equation in the following problem, and find its solution (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.

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 units digit of the number be x.

And the tens digit is y.

So the real number will be = 10y + x,

And reversed number = 10x + y

Situation I

x + y = 9       ...(i)

Situation II

9(number) = 2(flipped number)

or 9(10y + x) = 2(10x + y)

or 90y + 9x = 20x + 2y

or 20x – 9x + 2y – 90y = 0

or 11x – 88y = 0

or x – 8y = 0

or x = 8y           ...(ii)

By substituting x = 8y in equation (i)

x + y = 9

or 8y + y = 9

or 9y = 9

or y = 1

Substituting y = 1 into equation two

x = 8y = 8 × 1 = 8

Hence, required number = 10y + x

= 10 × 1 + 8

= 18