Q

# 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

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.

Views

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.

Exams
Articles
Questions