Solve the following systems of equations:

Question:

Solve the following systems of equations:

$\frac{3}{x}-\frac{1}{y}=-9$

$\frac{2}{x}+\frac{3}{y}=5$

Solution:

The given equations are:

$\frac{3}{x}-\frac{1}{y}=-9$ $\ldots(i)$

$\frac{2}{x}+\frac{3}{y}=5 \ldots(i i)$

Multiply equation $(i)$ by 3 and add both equations, we get

$\frac{9}{x}-\frac{3}{y}=-27$

Put the value of $x$ in equation $(i)$, we get

$\frac{3}{\frac{-1}{2}}-\frac{1}{y}=-9$

$\Rightarrow \frac{-1}{y}=-3$

$\Rightarrow y=\frac{1}{3}$

Hence the value of $x=-\frac{1}{2}$ and $y=\frac{1}{3}$

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