The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number

Question

Form the pair of linear equations in the following problems, and find their solutions (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.

Answer 1

Let the two digit number is 10x + y.

Sum of the digits of to digit number is

x + y = 9 ………….. (i)

Number obtained by reversing the order of the digits, we get 10y + x.

Twitching the 10y + x, it is nine times of first number.

∴ 2(10y + x) = 9(10x + 4)

20y + 2x = 90x + 9y

2x – 90x + 20y – 9y = 0

-88x + 11y = 0

88x – 11y = 0

8x – y = 0 ………….. (ii)

By adding eqn. (i) to eqn. (ii),

Substituting the value of ‘x’ in eqn. (i),

x + y = 9

1 + y = 9

y = 9 – 1

y = 8

∴ x = 1, y = 8

∴ Two digit number = 10x + y

= 10 × 1 + 8

= 10 + 8

=18.