Question

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

Please show the answer with calculations and steps.

Answer 1

let the digit at once place be Y ,
and,the digit at tens place be X
The number obtained is 10X+ Y
then ,according to question:-
X+Y = 9............(i)
Now ,if we reverse the order of digit then,number will be 10Y + X,
9(10X+Y)= 2(10Y+X)
= 90X+9Y = 20Y +2X
= 88X- 11Y = 0
= 8(8X-Y) = 0
= 8X-Y = 0/8
= 8X-Y = 0.................(ii)
Adding equation (i) and (ii).
=X+Y +8x-Y = 9
=9X = 9
=X = 1
Hence ,putting the value of X in any equation ,
=8(1)-Y =0
= Y= 8
Hence,the no. formed = 10X + Y = 10(1)+8= 18