Đáp án:
$\begin{array}{l}
Do:x + y = 540\\
\Rightarrow x = 540 - y\\
Thay\,vào:\dfrac{{100}}{x} - \dfrac{{120}}{y} = 1\\
\Rightarrow \dfrac{{100}}{{540 - y}} - \dfrac{{120}}{y} = 1\\
\Rightarrow \dfrac{{100y - 120.\left( {540 - y} \right)}}{{\left( {540 - y} \right).y}} = 1\\
\Rightarrow 100y - 64800 + 120y = - {y^2} + 540y\\
\Rightarrow {y^2} - 320y - 64800 = 0\\
\Rightarrow \left[ \begin{array}{l}
y = 160 - 20\sqrt {226} \\
y = 160 + 20\sqrt {226}
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = 380 + 20\sqrt {226} \\
x = 380 - 20\sqrt {226}
\end{array} \right.\\
Vậy\,\left( {x;y} \right) = \left\{ \begin{array}{l}
\left( {380 + 20\sqrt {226} ;160 - 20\sqrt {226} } \right);\\
\left( {\left( {380 - 20\sqrt {226} ;160 + 20\sqrt {226} } \right)} \right)
\end{array} \right\}
\end{array}$
