\(\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{5}{36}\\\dfrac{4}{x}+\dfrac{3}{y}=\dfrac{1}{2}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{4}{x}+\dfrac{4}{y}=\dfrac{5}{9}\\\dfrac{4}{x}+\dfrac{3}{y}=\dfrac{1}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{1}{y}=\dfrac{1}{18}\\\dfrac{1}{x}=\dfrac{1}{36}-\dfrac{1}{18}=-\dfrac{1}{36}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=18\\x=-36\end{matrix}\right.\)