$\frac{x}{y}+\frac{y}{x}=-2\Rightarrow \frac{{{x}^{2}}+{{y}^{2}}}{xy}=-2\Rightarrow {{x}^{2}}+{{y}^{2}}+2xy=0\Rightarrow {{(x+y)}^{2}}=0$ در نتیجه: $x+y=0\Rightarrow y=-x\,\,\,\,\,\,\,\,\,\,\,\,\,x\ne 0\,\,\,\,,\,\,\,\,y\ne 0$ بنابراین y تابعی از x است. $\left\{ \begin{matrix}   y+2y+3=x\,\,\,\,\,\,\,\,\,y\ge -\frac{3}{2}  \\   y-2y-3=x\,\,\,\,\,\,\,\,\,y