$\begin{array}{l} \left\{ \begin{array}{l} 4x + \dfrac{{9y}}{4} = 210(1)\\ \dfrac{{9y}}{{4x}} = \frac{{4x}}{y}(2) \end{array} \right.(2) \Rightarrow 9{y^2} = 16{x^2} \Leftrightarrow \left[ \begin{array}{l} 3y = 4x\\ 3y = - 4x \end{array} \right.\\ (1) \Rightarrow 4x + \frac{{9y}}{4} = 210 \Leftrightarrow 16x + 9y = 840 \Leftrightarrow \left[ \begin{array}{l} \left\{ \begin{array}{l} 12y + 9y = 840\\ 3y = 4x \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} y = 40\\ x = 30 \end{array} \right.\\ \left\{ \begin{array}{l} 16x - 12x = 840\\ 3y = - 4x \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} x = 210\\ y = - 280 \end{array} \right. \end{array} \right. \Rightarrow \left( {x;y} \right) = \left( {30;40} \right),\left( {210; - 280} \right) \end{array}$
