UPSC 2014 CDS II Math Paper

x+y

x−y

=

3

5

⇒5x+5y=3x−3y
⇒2x=−8y⇒x=−4y
Therefore, either x is positive and y is negative or x is negative and y is positive. But, it is given that xy is positive. This is not possible as x and y cannot be simultaneously positive or negative.
Thus, there exists no real solutions for x and y