Đáp án:
\(\left\{ \begin{array}{l}
y = \dfrac{{\sqrt 2 + \sqrt {10} }}{5}\\
x = \dfrac{{4 - \sqrt 5 }}{5}
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
\left\{ \begin{array}{l}
x - 2\sqrt 2 y = \sqrt 5 \\
x\sqrt 2 + y = \sqrt 2
\end{array} \right.\\
\to \left\{ \begin{array}{l}
- x\sqrt 2 + 4y = \sqrt {10} \\
x\sqrt 2 + y = \sqrt 2
\end{array} \right.\\
\to \left\{ \begin{array}{l}
5y = \sqrt 2 + \sqrt {10} \\
x\sqrt 2 + y = \sqrt 2
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = \dfrac{{\sqrt 2 + \sqrt {10} }}{5}\\
x = \dfrac{{\sqrt 2 - y}}{{\sqrt 2 }}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
y = \dfrac{{\sqrt 2 + \sqrt {10} }}{5}\\
x = \dfrac{{4 - \sqrt 5 }}{5}
\end{array} \right.
\end{array}\)
