exo7 1168

Résoudre et discuter suivant les valeurs de $b_1$, $b_2$, $b_3$ et $b_4$ : $$\begin{gathered} (S_1)\;\left\{\begin{array}{rcl} x+3y+4z+7t &=&b_1 \\ x+3y+4z+5t &=&b_2 \\ x+3y+3z+2t &=&b_3 \\ x+y+z+t &=&b_4 \end{array}\right. \qquad(S_2)\;\left\{\begin{array}{rcl} x+3y+5z+3t &=&b_1 \\ x+4y+7z+3t &=&b_2\\ y+2z &=& b_3\\ x+2y+3z+2t &=&b_4 \end{array}\right.\\ (S_3)\;\left\{\begin{array}{rcl} x+y+2z-t &=&b_1 \\ -x+3y+t &=&b_2 \\ 2x-2y+2z-2t &=&b_3 \\ 2y+z&=&b_4\\ \end{array}\right. \qquad(S_4)\;\left\{\begin{array}{rcl} x+2y+z+2t &=&b_1 \\ -2x-4y-2z-4t &=&b_2\\ -x-2y-z-2t &=& b_3\\ 3x+6y+3z+6t &=&b_4 \end{array}\right.\end{gathered}$$