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.
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