\(\frac{1}{x}+\frac{-y}{2}=\frac{y}{2}\)
\(\Leftrightarrow\frac{1}{x}=\frac{y}{2}-\frac{-y}{2}\)
\(\Leftrightarrow\frac{1}{x}=\frac{y}{2}+\frac{y}{2}\)
\(\Leftrightarrow\frac{1}{x}=\frac{y+y}{2}\)
\(\Leftrightarrow\frac{1}{x}=\frac{2y}{2}\)
\(\Leftrightarrow\frac{1}{x}=y\)
\(\Leftrightarrow xy=1\)
\(\Leftrightarrow x=y=1\)