Giải hệ phương trình \(\left\{ \begin{array}{l}x - y = 5\\{x^2} + {y^2} + xy = 7\end{array} \right.\) 

* Hướng dẫn giải

\(\begin{array}{l}
\left\{ \begin{array}{l}
x - y = 5\\
{x^2} + {y^2} + xy = 7
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = y + 5\\
{\left( {y + 5} \right)^2} + {y^2} + \left( {y + 5} \right)y = 7
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x = y + 5\\
3{y^2} + 15y + 18 = 0
\end{array} \right.\\
\left\{ \begin{array}{l}
\left[ \begin{array}{l}
y =  - 2\\
y =  - 3
\end{array} \right.\\
x = y + 5
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x = 3\\
y =  - 2
\end{array} \right.\\
\left\{ \begin{array}{l}
x = 2\\
y =  - 3
\end{array} \right.
\end{array} \right.
\end{array}\)