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Q2.    Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method :

                (iii) 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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Let the unit digit of the number be x and 10's digit be y.

Now, According to the question,

x+y=9.......(1)24323

Also

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

\Rightarrow 90y+9x=20x+2y

\Rightarrow 88y-11x=0

\Rightarrow 8y-x=0.........(2)

Now adding (1) and (2) we get,

\Rightarrow 9y=9

\Rightarrow y=1

now putting this value in (1)

x+1=9

\Rightarrow x=8

Hence the number is 18.

 

Posted by

Pankaj Sanodiya

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