If $\frac{x+1}{y} = \frac{1}{2}, \frac{x}{y-2} = \frac{1}{2}$, find x and y.

Given :

The given terms are  $\frac{x+1}{y} = \frac{1}{2}, \frac{x}{y-2} = \frac{1}{2}$.

To do :

We have to find the values of x and y.

Solution :

 $\frac{x+1}{y} = \frac{1}{2}$

$2(x+1) = 1(y)$       [cross multiplication]

$2x + 2 = y$

$2x - y + 2 = 0$.................(i)

$\frac{x}{y-2} = \frac{1}{2}$

$2(x) = 1(y-2)$     [cross multiplication]

$2x = y-2$

$2x - y + 2 = 0$

The same line is written in two different forms. Therefore, the given system of equations has infinite solutions.

$(x,y) = (-1,0), (x,y) = (0,2)$ are two different solutions of the given system of equations.