Question

i) The sum of the two digit number is 9. Also, 9 times this number is twice the number obtained by reversing the order of the digits. Find the number.

ii) for which values of 'a' and 'b' does the following pair of linear equations have an infinity number of solutions?

(a-b)x+(a+b)y=3a+b-2

2x+3y=7

Answer 1

Let the two-digit number be “ab”

Then the number is of the form 10a + b

According to given condition,

a+b=9……(i)

Also,

9(10a+b)=2(10b+a)

90a+9b=20b+2a

⇒8a–b=0……(ii)

Solving (i) and (ii),

a=9−b [From (i)]

Substituting value of a in (ii)

8a–b=0

8(9−b)−b=0

−9b=−72⇒b=8

Now, a=9−b

⇒a=9−8=1

∴a=1,b=8

∴ required number is 18

Dear student
don't ask multiple questions. So you please ask the second question as a new question