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?
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
Is there an error in this question or solution?