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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.

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#### Solution

Let the unit digit and tens digits of the number be x and y respectively. Then, number = 10y + x Number after reversing the digits = 10x + y

According to the given information,

x + y = 9... (1)

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

88y - 11x = 0

- x + 8y =0.....(2)

Adding equation (1) and (2), we obtain

9y = 9

y = 1 (3)

Substituting the value in equation (1), we obtain

x = 8

Hence, the number is 10y + x = 10 × 1 + 8 = 18

Is there an error in this question or solution?