\(\left\{{}\begin{matrix}\frac{a}{5}+\frac{b}{3}=-\frac{1}{3}\\4a-5b-10=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\frac{a}{5}=\frac{-1-b}{3}\\4a-5b=10\end{matrix}\right.\)
\(\left\{{}\begin{matrix}a=\frac{-5\left(1+b\right)}{3}\\\frac{4.\left(-5\right)\left(1+b\right)}{3}-5b=10\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=\frac{-5\left(1+b\right)}{3}\\-20-20b-15b=30\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}a=\frac{-5\left(1+b\right)}{3}\\-35b=50\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=\frac{-5\left(1-\frac{10}{7}\right)}{3}=\frac{5}{7}\\b=-\frac{10}{7}\end{matrix}\right.\)
