$\begin{array}{l} \left\{ \begin{array}{l} x = 2y - 3\\ y = 2x - 3 \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} x - 2y = - 3\\ 2x - y = 3 \end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l} 2x - 4y = - 6\\ 2x - y = 3 \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} - 3y = - 9\\ y = 2x - 3 \end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l} x = 3\\ y = 3 \end{array} \right. \to \left( {x;y} \right) = \left( {3;3} \right) \end{array}$
