\(\left\{{}\begin{matrix}13x-y=5\\5x+2y=23\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=13x-5\\5x+2y=23\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=13x-5\\5x+2\left(13x-5\right)=23\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=13x-5\\31x-10=23\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}31x=33\\y=13x-5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{33}{31}\\y=13\cdot\dfrac{33}{31}-5=\dfrac{274}{31}\end{matrix}\right.\)