exo4.tex

%@Dif:3
Résous les systèmes suivants :
$\begin{array}{cp{0cm}|p{0cm}cp{0cm}|p{0cm}c} \left\{\begin{tabular}{l} x-y=8\\ \\ 7x+5y=104\\ \end{tabular} \right.&&& \left\{\begin{tabular}{l} 3x+y=8\\ \\ 7x+4y=104\\ \end{tabular} \right.&&& \left\{\begin{tabular}{l} 4x+7y=209\\ \\ 2x+5y=121\\ \end{tabular} \right.\\ &&&&&\\ \mbox{Solution : }(12;4)&&&\mbox{Solution : }(-14.4,51.2)&&&\mbox{Solution : }(33;11)\\ \\ \hline \\ \left\{\begin{tabular}{l} 5x+3y=136\\ \\ 2x+6y=112\\ \end{tabular} \right.&&& \left\{\begin{tabular}{l} 2x+3y=60\\ \\ 3x+2y=70\\ \end{tabular} \right.&&& \left\{\begin{tabular}{l} 3x+5y=24,80\\ \\ 4x+7y=34\\ \end{tabular} \right. \\ &&&&&\\ \mbox{Solution : }(20;12)&&&\mbox{Solution : }(18;8)&&&\mbox{Solution : }(3,6;2,8)\\ \\ \hline \\ \left\{\begin{tabular}{l} x-3y=7\\ 2x+5y=25\\ \end{tabular} \right.&&& \left\{\begin{tabular}{l} 4x-5y=13\\ 9x+y=17\\ \end{tabular} \right.&&& \left\{\begin{tabular}{l} 5x-4y=-26\\ 4x-5y=-28\\ \end{tabular} \right.\\ &&&&&\\ \mbox{Solution : }(10;1)&&&\mbox{Solution : }(2;-1)&&&\mbox{Solution : }(-2;4)\\ \\ \hline \\ \left\{\begin{tabular}{l} -2x+3y=4\\ 5x-5y=5\\ \end{tabular} \right.&&& \left\{\begin{tabular}{l} 5x+4y=-26\\ 4x-4y=-28\\ \end{tabular} \right. &&& \left\{\begin{tabular}{l} -2x-3y=4\\ 5x-5y=5\\ \end{tabular} \right.\\ &&&&&&\\ \mbox{Solution : }(7;6)&&&\mbox{Solution : }(-6;1)&&&\mbox{Solution : }(-2;-1.2)\\ \\ \hline \\ \left\{\begin{tabular}{l} x+2y=8\\ 2x-3y=2\\ \end{tabular} \right.&&& \left\{\begin{tabular}{l} 4x-3y=1\\ 5x+2y=7\\ \end{tabular} \right. &&& \left\{\begin{tabular}{l} 4x-3y=2\\ 12x-6y=3\\ \end{tabular} \right.\\ &&&&&&\\ \mbox{Solution : }(4;2)&&&\mbox{Solution : }(1;1)&&&\mbox{Solution : }\left(-\dfrac{1}{4};-1\right)\\ \\ \hline \\ \left\{\begin{tabular}{l} 4x+5y=21\\ 3x+y=8\\ \end{tabular} \right.&&&\left\{\begin{tabular}{l} 3,5x+4,2y=14\\ 1,2x-0,3y=-3,9\\ \end{tabular} \right.&&& \left\{\begin{tabular}{l} 5x-2y-7=0\\ 2x+4y=22\\ \end{tabular} \right.\\ &&&&&&\\ \mbox{Solution : }\left(\dfrac{19}{11};\dfrac{31}{11}\right)&&&\mbox{Solution : }(-2;5)&&&\mbox{Solution : }(3;4)\\ \end{array}$
%@Commentaire: Résolution de systèmes en autonomie.