Answer
$x=\dfrac{1}{5}$
and $y=\dfrac{1}{3}$
Work Step by Step
Consider our first equation: $\dfrac{2}{x}-\dfrac{3}{y}=1$
This gives: $xy=2y-3x$ ...(1)
Next, consider our second equation: $\dfrac{-4}{x}+\dfrac{7}{y}=1$
This gives: $xy=-4y-7x$ ...(2)
Now, equate both equations (1) and (2), we get
$2y-3x=-4y-7x$
or, $3y=5x \implies y=\dfrac{5x}{3}$
Plug $y=\dfrac{5x}{3}$ in the first equation , we get
$\dfrac{2}{x}-\dfrac{3}{\dfrac{5x}{3}}=1 \implies \dfrac{10-9}{5x}=1$
This gives: $5x =1 \implies x=\dfrac{1}{5}$
Thus, $y=\dfrac{5(\dfrac{1}{5})}{3}=\dfrac{1}{3}$
