$\left\{\begin{array}{l} 3x+y=m+3\\ x+2y=2m+1\end{array} \right.\\ <=>\left\{\begin{array}{l} 6x+2y=2m+6\\ x+2y=2m+1\end{array} \right.\\ <=>\left\{\begin{array}{l} 6x+2y-(x+2y)=2m+6-(2m+1)\\ x+2y=2m+1\end{array} \right.\\ <=>\left\{\begin{array}{l} 5x=5\\ x+2y=2m+1\end{array} \right.\\ <=>\left\{\begin{array}{l} x=1\\ y=m\end{array} \right.\\ a)m=2=>\left\{\begin{array}{l} x=1\\ y=2\end{array} \right.\\ b)2y^2+x-1=0\\ <=>2m^2=0\\ <=>m=0$