$\begin{array}{l} \left\{ \begin{array}{l} 2{x^2} + 2{y^2} - xy = 5\\ 2x - 2y - xy = 5 \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} 2{\left( {x - y} \right)^2} + 3xy = 5\\ 2\left( {x - y} \right) - xy = 5 \end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l} 2{a^2} + 3b = 5\\ 2a - b = 5 \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} 2{a^2} + \left( {2a - 5} \right).3 = 5\\ 2a - b = 5 \end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l} 2{a^2} + 6a - 20 = 0\\ 2a - b = 5 \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} \left[ \begin{array}{l} a = 2\\ a = - 5 \end{array} \right.\\ b = 2a - 5 \end{array} \right.\\ \Leftrightarrow \left[ \begin{array}{l} \left\{ \begin{array}{l} a = 2\\ b = - 1 \end{array} \right.\\ \left\{ \begin{array}{l} a = - 5\\ b = - 15 \end{array} \right. \end{array} \right.\\ + a = 2,b = - 1 \Rightarrow \left\{ \begin{array}{l} x - y = 2\\ xy = - 1 \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} x\left( {2 + x} \right) = - 1\\ y = x + 2 \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} {\left( {x + 1} \right)^2} = 0\\ y = x + 2 \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} x = - 1\\ y = 1 \end{array} \right.\\ a = - 5,b = - 15 \Rightarrow \left\{ \begin{array}{l} xy = - 15\\ x - y = - 5 \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} x = y - 5\\ \left( {y - 5} \right)y = - 15 \end{array} \right. \Rightarrow PTVN\\ \left( {x;y} \right) = \left( { - 1;1} \right)\\ \left\{ \begin{array}{l} x + y + xy = 3\\ {x^2} + {y^2} = 2 \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} S + P = 3\\ {S^2} - 2P = 2 \end{array} \right.\left( {S = x + y,P = xy,{S^2} - 4P \ge 0} \right)\\ \Leftrightarrow \left\{ \begin{array}{l} P = 3 - S\\ {S^2} - 2\left( {3 - S} \right) = 2 \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} P = 3 - S\\ {S^2} + 2S - 8 = 0 \end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l} \left[ \begin{array}{l} S = 2\\ S = - 4 \end{array} \right.\\ P = 3 - S \end{array} \right. \Leftrightarrow \left[ \begin{array}{l} \left\{ \begin{array}{l} S = 2\\ P = 1 \end{array} \right.\\ \left\{ \begin{array}{l} S = - 4\\ P = 7 \end{array} \right.(L\,do\,{S^2} - 4P < 0) \end{array} \right.\\ + S = 2,P = 1\\ \Rightarrow \left\{ \begin{array}{l} x + y = 2\\ xy = 1 \end{array} \right. \Rightarrow \left\{ \begin{array}{l} y = 2 - x\\ x\left( {2 - x} \right) = 1 \end{array} \right. \Leftrightarrow \left\{ \begin{array}{l} y = 2 - x\\ {x^2} - 2x + 1 = 0 \end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l} x = 1\\ y = 1 \end{array} \right. \end{array}$
