Đáp án:
2) \(\left\{ \begin{array}{l}
x = 1\\
y = 3
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
1)\left\{ \begin{array}{l}
\sqrt 2 x + \sqrt 5 y = 2\\
x + \sqrt 5 y = 2
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\left( {1 - \sqrt 2 } \right)x = 2 - 2\\
x + \sqrt 5 y = 2
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = 0\\
y = \dfrac{2}{{\sqrt 5 }}
\end{array} \right.\\
2)DK:x \ge 0;y \ge 1\\
\left\{ \begin{array}{l}
\sqrt x + 2\sqrt {y - 1} = 5\\
4\sqrt x - \sqrt {y - 1} = 2
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\sqrt x + 2\sqrt {y - 1} = 5\\
8\sqrt x - 2\sqrt {y - 1} = 4
\end{array} \right.\\
\to \left\{ \begin{array}{l}
9\sqrt x = 9\\
\sqrt x + 2\sqrt {y - 1} = 5
\end{array} \right.\\
\to \left\{ \begin{array}{l}
\sqrt x = 1\\
2\sqrt {y - 1} = 4
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = 1\\
\sqrt {y - 1} = 2
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = 1\\
y - 1 = 2
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = 1\\
y = 3
\end{array} \right.
\end{array}\)