Question

form the pair of linear equation for the following problem and find its solution by elimination method:-
the sum of the digits of a 2digit no. is 9. Also, 9 times this no. is twice the no. obtained by reversing the order of the digits. gind the no.

please ans it asap

Answer 1

Given

Sum of two digits = 9

Let Ten's place digit = x

One's place digit = 9 - x

The original number = 10x + ( 9- x)

= 9x + 9 --------(1)

Reversing the digits we get new number =10 (9 - x )+ x

= 90 - 9x ------(2)
According to the problem

9 × (1) = 2 × (2)

9(90-9x) = 2(9x +9)

810 - 81x = 18x + 18

Divide each term with9

90 - 9x = 2x + 2

90 - 2 = 2x + 9x

88 = 11x

88/11= x

8= x

Therefore x=8

Required original number = 9x+9

= 9× 8 + 9

= 72 + 9

= 81

I hope this will useful to u

Answer 2

Sum of two digits = 9
Let Ten's place digit = x
One's place digit = 9 - x
The original number = 10x + ( 9- x)
= 9x + 9 --------(1)
Reversing the digits we get new number =10 (9 - x )+ x
= 90 - 9x ------(2)
According to the problem
9 × (1) = 2 × (2)
9(90-9x) = 2(9x +9)
810 - 81x = 18x + 18
Divide each term with9
90 - 9x = 2x + 2
90 - 2 = 2x + 9x
88 = 11x
88/11= x
8= x
Therefore x=8

Required original number = 9x+9
= 9× 8 + 9
= 72 + 9
= 81