2+x/3+2y=x-2/-2=3-5x/3-4y

$\begin{array}{l} \frac{{2 + x}}{{3 + 2y}} = \frac{{x - 2}}{{ - 2}}\\ \Rightarrow - 2(2 + x) = (x - 2)(3 + 2y)\\ \Rightarrow - 4 - 2x = 3x + 6xy - 6 - 4y\\ \Rightarrow 5x + 6xy - 4y - 2 = 0(1)\\ \\ \frac{{x - 2}}{{ - 2}} = \frac{{3 - 5x}}{{3 - 4y}}\\ \Rightarrow (x - 2)(3 - 4y) = - 2(3 - 5x)\\ \Rightarrow 3x - 4xy - 6 + 8y = - 6 + 10x\\ \Rightarrow 7x - 8y + 4xy = 0(2)\\ \\ (1) \times 2 - (2) \times 3 = 0\\ \Rightarrow 2(5x + 6xy - 4y - 2) - 3(7x - 8y + 4xy) = 0\\ \Rightarrow - 11x + 16y - 4 = 0\\ \Rightarrow x = \frac{{16y - 4}}{{11}}\\ (1) \Rightarrow 5\frac{{16y - 4}}{{11}} + 6\frac{{16y - 4}}{{11}}y - 4y - 2 = 0\\ \Rightarrow 16{y^2} + 2y - 7 = 0\\ \Rightarrow \left[ \begin{array}{l} y = \frac{{ - 1 + \sqrt {113} }}{{16}}\\ y = \frac{{ - 1 - \sqrt {113} }}{{16}} \end{array} \right. \end{array}$