Đáp án:
\(\left[ \begin{array}{l}
\left\{ \begin{array}{l}
x = 3\\
y = - 1
\end{array} \right.\\
\left\{ \begin{array}{l}
x = 1\\
y = - 3
\end{array} \right.\\
\left\{ \begin{array}{l}
x = 1\\
y = - 1
\end{array} \right.
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
\left\{ \begin{array}{l}
x + xy - y = 1\\
{x^2} + {y^2} - 4(x - y) = - 6
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
xy + (x - y) = 1\\
{(x - y)^2} - 4(x - y) + 2xy = - 6
\end{array} \right.\\
x - y = a,xy = b\\
\Rightarrow \left\{ \begin{array}{l}
b + a = 1\\
{a^2} - 4a + 2b = - 6
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
b = 1 - a\\
{a^2} - 4a + 2(1 - a) = - 6
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
b = 1 - a\\
\left[ \begin{array}{l}
a = 4\\
a = 2
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
a = 4,b = - 3\\
a = 2,b = - 1
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x - y = 4\\
xy = - 3
\end{array} \right.\\
\left\{ \begin{array}{l}
x - y = 2\\
xy = - 1
\end{array} \right.
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
x = 3\\
y = - 1
\end{array} \right.\\
\left\{ \begin{array}{l}
x = 1\\
y = - 3
\end{array} \right.\\
\left\{ \begin{array}{l}
x = 1\\
y = - 1
\end{array} \right.
\end{array} \right.
\end{array}\)
