The difference between two numbers is 26 and one number is three times the other. Find them.

Question

Form the pair of linear equations for the following problems and find their solution by elimination method:

The difference between two numbers is 26 and one number is three times the other. Find them.

Answer 1

Let the one number = x

And the other number = y

According to the question,

x – y = 26 …(i)

and x = 3y

or x – 3y = 0 …(ii)

Now, we can solve this by an elimination method

On subtracting Eq. (ii) from (i) we get

x – 3y – x + y = 0 – 26

⇒ – 3y + y = – 26

⇒ – 2y = – 26

⇒ y = 13

On putting y = 13 in Eq. (ii) we get

x – 3(13) = 0

⇒ x – 39 = 0

⇒ x = 39

Hence, the two numbers are 39 and 13.