Đáp án:
\(\left\{ \begin{array}{l}
x = \frac{{3\sqrt 5 }}{5}\\
y = \frac{{ - 10 + \sqrt 5 }}{5}
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
\left\{ \begin{array}{l}
3\left( {\sqrt 5 + 1} \right)x + 6y = 3\left( {\sqrt 5 - 1} \right)\\
2\left( {\sqrt 5 - 1} \right)x + 6y = - 6
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\left( {5 + \sqrt 5 } \right)x = 3 + 3\sqrt 5 \\
2\left( {\sqrt 5 - 1} \right)x + 6y = - 6
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \frac{{3 + 3\sqrt 5 }}{{5 + \sqrt 5 }}\\
2\left( {\sqrt 5 - 1} \right)x + 6y = - 6
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \frac{{3\sqrt 5 }}{5}\\
y = \frac{{ - 10 + \sqrt 5 }}{5}
\end{array} \right.
\end{array}\)
