\(\left\{\begin{array}{ccc}4x+5y=13\\8x-2y=14\end{array}\right\\\begin{array}{ccc}(i)\\(ii)\end{array}\left[\begin{array}{ccc}4&5\\8&-2\end{array}\right\left|\begin{array}{ccc}13\\14\end{array}\right]\xrightarrow{(i):4}\left[\begin{array}{ccc}1&\frac{5}{4}\\8&-2\end{array}\right\left|\begin{array}{ccc}\frac{13}{4}\\14\end{array}\right]\xrightarrow{(ii)-8(i)}\)
\(\left[\begin{array}{ccc}1&\frac{5}{4}\\0&-12\end{array}\right\left|\begin{array}{ccc}\frac{13}{4}\\-12\end{array}\right]\xrightarrow{(ii):(-12)}\\\left[\begin{array}{ccc}1&\frac{5}{4}\\0&1\end{array}\right\left|\begin{array}{ccc}\frac{13}{4}\\1\end{array}\right]\xrightarrow{(i)-(ii)\cdot\frac{5}{4}}\)
\(\left[\begin{array}{ccc}1&0\\0&1\end{array}\right\left|\begin{array}{ccc}2\\1\end{array}\right]\\\\Answer:\boxed{ \left \{ {{x=2} \atop {y=1}} \right. \to\fbox{D.}}\)
