Đáp án: $\,\left( {x;y} \right) = \left\{ {\left( {32;10} \right);\left( {\dfrac{{10}}{3};96} \right)} \right\}$
Giải thích các bước giải:
$\begin{array}{l}
\left\{ \begin{array}{l}
x.y = 320\\
\left( {x + 1} \right)\left( {y + 3} \right) = 429
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x.y = 320\\
x.y + 3x + y + 3 = 429
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x.y = 320\\
3x + y = 429 - 3 - 320 = 106
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x.y = 320\\
y = 106 - 3x
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
x.\left( {106 - 3x} \right) = 320\\
y = 106 - 3x
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
y = 106 - 3x\\
3{x^2} - 106x + 320 = 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
y = 106 - 3x\\
\left( {3x - 10} \right)\left( {x - 32} \right) = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 32;y = 10\\
x = \dfrac{{10}}{3};y = 96
\end{array} \right.\\
Vậy\,\left( {x;y} \right) = \left\{ {\left( {32;10} \right);\left( {\dfrac{{10}}{3};96} \right)} \right\}
\end{array}$
