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

If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes 1/2 if we only add 1 to the denominator. What is the fraction?

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#### Solution

Let the fraction be `x/y`

According to the given information,

`(x+1)/(y-1)=1` ⇒ x - y = -2 (1)

`x/(y+1) = 1/2` ⇒ 2x-y = 1 (2)

Subtracting equation (1) from equation (2), we obtain

x = 3 (3)

Substituting this value in equation (1), we obtain

3 - y = -2

-y = -5

y = 5

Hence the fraction is `3/5`

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Elimination Method

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