$\begin{array}{l} \left\{ \begin{array}{l} \left( {\sqrt x + 2} \right)\left( {1 - \sqrt y } \right) = 4\\ \dfrac{{\sqrt x - \sqrt y }}{{\sqrt x + 2}} = \dfrac{1}{2} \end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l} \sqrt x - \sqrt {xy} + 2 - 2\sqrt y = 4\\ 2\sqrt x - 2\sqrt y = \sqrt x + 2 \end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l} \sqrt x - \sqrt {xy} - 2\sqrt y = 2\\ \sqrt x - 2\sqrt y = 2 \end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l} \sqrt x = 2\sqrt y + 2\left( 1 \right)\\ \sqrt x - \sqrt {xy} - 2\sqrt y = 2\left( 2 \right) \end{array} \right.\\ \left( 1 \right) \to \left( 2 \right):2\sqrt y + 2 - \left( {2\sqrt y + 2} \right)\sqrt y - 2\sqrt y = 2\\ \Leftrightarrow - 2y - 2\sqrt y = 0\\ \Leftrightarrow 2y + 2\sqrt y = 0\\ \Leftrightarrow 2\sqrt y \left( {\sqrt y + 1} \right) = 0\\ \Leftrightarrow \left[ \begin{array}{l} \sqrt y = 0\\ \sqrt y + 1 = 0 \end{array} \right. \Rightarrow \left\{ \begin{array}{l} y = 0\\ \sqrt x = 2\sqrt 0 + 2 \end{array} \right. \Rightarrow \left[ \begin{array}{l} y = 0\\ x = 4 \end{array} \right.\\ \Rightarrow \left( {x;y} \right) = \left( {4;0} \right) \end{array}$
