Q7 of 186 Page 4

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.

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.


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