Réponse :
Bonsoir,
Explications étape par étape
1) Par combinaison linéaire
[tex]\left\{\begin {array} {ccc|c|c}3x-4y&=&-1&5&2\\-2x+5y&=&2&4&3\\\end{array}\right.\\\\\\\left\{\begin {array} {ccc}7x&=&3\\\\7y&=&4\\\end{array}\right.\\\\\\\boxed{\left\{\begin {array} {ccc}x&=&\dfrac{3}{7}\\\\y&=&\dfrac{4}{7}\\\end{array}\right.\\}\\[/tex]
2) Méthode de Cramer
[tex]\left\{\begin {array} {ccc}-4x+3y&=&2\\-2x+5y&-3\\\end{array}\right.\\\\\\\Delta=\left\\\begin{array}{|cc|}-4&3\\-2&5\\\end{array}\right. = -10+6=-14\\\\\\\Delta_1 =\left\\\begin{array}{|cc|}2&3\\-3&5\\\end{array}\right. = 10+9=19\\\\\\\Delta_2 =\left\\\begin{array}{|cc|}-4&2\\-2&-3\\\end{array}\right. =12+4=16\\\\\\\boxed{\left\{\begin{array}{ccc}x&=-&\dfrac{19}{14}\\\\y&=-&\dfrac{16}{14}\\\end{array}\right.\\}\\[/tex]
3) Par élimination
[tex]\left\{\begin{array}{ccc}3x-y&=&1\\-2x+3y&=&2\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}y&=&3x-1\\-2x+3(3x-1)&=&2\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}7x&=&5\\\\y&=&3*\dfrac{5}{7} -1\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x&=&\dfrac{5}{7} \\\\y&=&\dfrac{8}{7}\\\end{array}\right.\\\\[/tex]
d) équation impossible
[tex]\left\{\begin{array}{ccc}3x-2y&=&-1\\\\-3x+2y&=&2\\\end{array}\right.\\\\\\Somme\ des\ 2\ \' equations\\0*x+0*y=1 \Longrightarrow\ 0=1\ impossible[/tex]
