\(\left\{{}\begin{matrix}2xy=30\\x^2-y^2=16\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\frac{15}{y}\\\left(\frac{15}{y}\right)^2-y^2=16\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\frac{15}{y}\\\frac{225}{y^2}-y^2=16\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\frac{15}{y}\\225-y^4=16y^2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\frac{15}{y}\\y^4+16y^2-225=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\frac{15}{y}\\\left(y^2-9\right)\left(y^2+25\right)=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\frac{15}{y}\\\left[{}\begin{matrix}y^2=9\\y^2=-25\end{matrix}\right.\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\frac{15}{3}=5\\y=3\end{matrix}\right.\)
