Réponse :
Bonjour,
Explications étape par étape :
[tex]\left\{\begin{array}{ccc}3x-5y+7z&=&5\\2x+3y-6z&=&1\\1x+1y-1z&=&1\\\end{array}\right.\\\\\\\Delta=\left| \begin{array}{ccc}3&-5&7\\2&3&6\\1&1&-1\\\end{array}\right| = \left| \begin{array}{ccc} 0&-8&10\\ 0&1&-4\\ 1&1&-1\\ \end{array}\right| = 32-10=22\\\\[/tex]
[tex]\Delta_1=\left| \begin{array}{ccc}5&-5&7\\1&3&-6\\1&1&-1\\\end{array}\right| =\left| \begin{array}{ccc}0&-20&37\\0&2&-5\\1&1&-1\\\end{array}\right| =100-74=26\\\\[/tex]
[tex]\Delta_2=\left| \begin{array}{ccc}3&5&7\\2&1&-6\\1&1&-1\\\end{array}\right|=\left| \begin{array}{ccc}0&2&10\\0&-1&-4\\1&1&-1\end{array}\right|=-8+10=2\\\\[/tex]
[tex]\Delta_3=\left| \begin{array}{ccc}3&-5&5\\2&3&1\\1&1&1\\\end{array}\right|=\left| \begin{array}{ccc}0&-8&2\\0&1&-1\\1&1&1\\\end{array}\right|=8-2=6\\\\\\[/tex]
[tex]\left\{\begin{array}{ccc}x&=&\dfrac{26}{22}=\dfrac{13}{11}\\\\y&=&\dfrac{2}{22}=\dfrac{1}{11}\\\\z&=&\dfrac{6}{22}=\dfrac{3}{11}\\\\\end {array}\\[/tex]
