Bonjour,
[tex]1) \left\{ \begin{array}{ll} x+y=4\\ 2x+3y=7 \end{array}\right[/tex] ⇔ [tex]\left\{ \begin{array}{ll} x=4-y\\ 2x+3y=7 \end{array}\right[/tex] ⇔ [tex]\left\{ \begin{array}{ll} x+y=4\\ 2(4-y)+3y=7 \end{array}\right[/tex] ⇔ [tex]\left\{ \begin{array}{ll} x+y=4\\ 8-2y+3y=7 \end{array}\right[/tex]
⇔ [tex]\left\{ \begin{array}{ll} x+y=4\\ 8+y=7 \end{array}\right[/tex] ⇔ [tex]\left\{ \begin{array}{ll} x+y=4\\ y=7-8 \end{array}\right[/tex] ⇔ [tex]\left\{ \begin{array}{ll} x+y=4\\ y=-1 \end{array}\right[/tex] ⇔ [tex]\left\{ \begin{array}{ll} x+(-1)=4\\ y=-1 \end{array}\right[/tex]⇔ [tex]\left\{ \begin{array}{ll} x=5\\ y=-1 \end{array}\right[/tex]
[tex]2) \left\{ \begin{array}{ll} x-2y=4\\ 2x+3y=-6 \end{array}\right[/tex] ⇔ [tex]\left\{ \begin{array}{ll} x=4+2y\\ 2x+3y=-6 \end{array}\right[/tex] ⇔ [tex]\left\{ \begin{array}{ll} x-2y=4\\ 2(4+2y)+3y=-6 \end{array}\right[/tex] ⇔ [tex]\left\{ \begin{array}{ll} x-2y=4\\ 8+ 4y + 3y = -6 \end{array}\right[/tex] ⇔ [tex]\left\{ \begin{array}{ll} x-2y=4\\ 8+7y=-6 \end{array}\right[/tex] ⇔ [tex]\left\{ \begin{array}{ll} x-2y=4\\ 7y=-6-8 \end{array}\right[/tex] ⇔ [tex]\left\{ \begin{array}{ll} x-2y=4\\ 7y=-14 \end{array}\right[/tex] ⇔ [tex]\left\{ \begin{array}{ll} x-2y=4\\ y=\frac{-14}{7} \end{array}\right[/tex] ⇔ [tex]\left\{ \begin{array}{ll} x-2y=4\\ y=-2 \end{array}\right[/tex] ⇔ [tex]\left\{ \begin{array}{ll} x-2\times(-2)=4\\ y=-2 \end{array}\right[/tex] ⇔ [tex]\left\{ \begin{array}{ll} x=0\\ y=-2 \end{array}\right[/tex]
Tu fais les suivants en faisant la même méthode ?
