[tex]\it \dfrac{7x-3y}{5}=\dfrac{5x-y}{3}-\dfrac{x+y}{2}|_{\cdot30} \Rightarrow 42x-18y=50x-10y-15x-15y \Rightarrow \\ \\ \\ \Rightarrow 42x+15x-50x-18y+10y+15y=0 \Rightarrow 7x+7y=0|_{:7} \Rightarrow x+y=0 \Rightarrow \\ \\ \\ \Rightarrow y=-x\ \ \ \ \ \ (1)\\ \\ \\\\ 3(x-1)=5(y+1) \Rightarrow 3x-3=5y+5 \Rightarrow 3x-5y=5+3\ \stackrel{(1)}{\Longrightarrow}8x=8 \Rightarrow \\ \\ \Rightarrow x=1\ \ \ \ \ \ (2)\\ \\ \\ (1),\ (2) \Rightarrow y=-1\\ \\ \\ S=\{(1,\ \ -1)\}[/tex]
