Résoudre (en discutant en fonction des différents paramètres) les systèmes suivants :
\[\begin{array}{ccc} 1)\;\left\{ \begin{array}{l} 2x+3y+z=4\\ -x+my+2z=5\\ 7x+3y+(m-5)z=7 \end{array} \right.& 2)\;\left\{ \begin{array}{l} 2x+my+z=3m\\ x-(2m+1)y+2z=4\\ 5x-y+4z=3m-2 \end{array} \right.& 3)\;\left\{ \begin{array}{l} x+y+z+t=3\\ x+my+z-mt=m+2\\ mx-y-mz-t=-1 \end{array} \right.\\ 4)\;\left\{ \begin{array}{l} x+2y+3z+mt=m-1\\ 2x+y+mz+3t=1\\ 3x+my+z+2t=0\\ mx+3y+2z+t=0 \end{array} \right.&5)\;\left\{ \begin{array}{l} mx+y+z=m+2\\ -x-y+mz=m-2\\ -mx+y+mz=-m\\ x-y-mz=m-4 \end{array} \right.&6)\; \left\{ \begin{array}{l} x+y+z=1\\ ax+by+cz=m\\ \frac{x}{a}+\frac{y}{b}+\frac{z}{c}=\frac{1}{m} \end{array} \right.\\ 7)\; \left\{ \begin{array}{l} (b+c)^2x+b^2y+c^2z=1\\ a^2x+(c+a)^2y+c^2z=1\\ a^2x+b^2y+(a+b)^2z=1 \end{array} \right.&8)\;\left\{ \begin{array}{l} ax+by+cz=p\\ cx+ay+bz=q\\ bx+cy+az=r \end{array} \right.& \\ 9)\;\left\{ \begin{array}{l} x+y+z=0\\ ax+by+cz=2\\ a^2x+b^2y+c^2z=3 \end{array} \right.&(\mbox{où}\;a,\;b,\;\mbox{et}\;c\;\mbox{sont les racines de l'équation}&t^3-t+1=0). \end{array}\]