Ta có: \(\left\{{}\begin{matrix}8x-7y=5\\12x+13y=-8\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}24x-21y=15\\24x+26y=-16\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-47y=31\\8x-7y=5\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=\dfrac{-31}{47}\\8x=5+7y=5+7\cdot\dfrac{-31}{47}=\dfrac{18}{47}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{9}{188}\\y=\dfrac{-31}{47}\end{matrix}\right.\)
Vậy: Hệ phương trình có nghiệm duy nhất là \(\left(x,y\right)=\left(\dfrac{9}{188};\dfrac{-31}{47}\right)\)