Đáp án:
\(\left[ \begin{array}{l}
y = 0\\
y = 5
\end{array} \right. \to \left[ \begin{array}{l}
x = 0\\
x = 7
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
\left\{ \begin{array}{l}
35\left( {x + y} \right) = 210\left( {x - y} \right)\\
210\left( {x - y} \right) = 12xy
\end{array} \right.\\
\to \left\{ \begin{array}{l}
35x + 35y = 210x - 210y\\
210x - 210y = 12xy
\end{array} \right.\\
\to \left\{ \begin{array}{l}
175x = 245y\\
210x - 210y = 12xy
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{7}{5}y\\
210.\dfrac{7}{5}y - 210y = 12.\dfrac{7}{5}y.y
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{7}{5}y\\
84y = \dfrac{{84}}{5}{y^2}
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{7}{5}y\\
\dfrac{{84}}{5}{y^2} - 84y = 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{7}{5}y\\
y\left( {\dfrac{{84}}{5}y - 84} \right) = 0
\end{array} \right.\\
\to \left\{ \begin{array}{l}
x = \dfrac{7}{5}y\\
\left[ \begin{array}{l}
y = 0\\
\dfrac{{84}}{5}y - 84 = 0
\end{array} \right.
\end{array} \right. \to \left[ \begin{array}{l}
y = 0\\
y = 5
\end{array} \right. \to \left[ \begin{array}{l}
x = 0\\
x = 7
\end{array} \right.
\end{array}\)
