2. Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:
(i) 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?
(i) Let the fraction be x/y
According to the question,x + 1/y - 1 = 1
⇒ x - y = -2 ... (i)x/y+1 = 1/2
⇒ 2x - y = 1 ... (ii)
Subtracting equation (i) from equation (ii), we get
x = 3 ... (iii)
Putting this value in equation (i), we get
3 - y = -2
-y = -5
y = 5
Hence, the fraction is 3/5
