Đáp án: (x;y) =(1;2) hoặc (2;1)
Giải thích các bước giải:
$\begin{array}{l}
\left\{ \begin{array}{l}
x + y + xy = 5\\
{x^2} + {y^2} = 5
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x + y = 5 - xy\\
{\left( {x + y} \right)^2} - 2xy = 5
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
x + y = 5 - xy\\
{\left( {5 - xy} \right)^2} - 2xy - 5 = 0
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
x + y = 5 - xy\\
{x^2}{y^2} - 12xy + 20 = 0
\end{array} \right.\\
\Rightarrow \left\{ \begin{array}{l}
x + y = 5 - xy\\
\left[ \begin{array}{l}
xy = 2\\
xy = 10
\end{array} \right.
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
xy = 2;x + y = 3\\
xy = 10;x + y = - 5\left( {vo\,nghiem} \right)
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = 1;y = 2\\
x = 2;y = 1
\end{array} \right.
\end{array}$
