Question

Solve: $\frac{1}{2x}-\frac{1}{y}=-1;\frac{1}{x}+\frac{1}{2y}=8$.

Answer 1

Given,

$\frac{1}{2x}-\frac{1}{y}=-1$........(1), $\frac{1}{x}+\frac{1}{2y}=8$......(2).

Now, dividing the equation (2) by $2$ and then subtracting (1) from it, we get,

$\frac{5}{4y}=5$

or, $y=\frac{1}{4}$.

Now, using the value of $y$ in (2) we get, $\frac{1}{x}=6$ or $x=\frac{1}{6}$.