Bonjour
Résoudre les systèmes :
2(x - y) - 3x = 4
-x + 2(x + y) = 0
2x - 2y - 3x = 4
-x + 2x + 2y = 0
(1) -x - 2y = 4
(2) x + 2y = 0
On additionne (1) et (2) :
-x - 2y + x + 2y = 4 + 0
0 = 4 impossible donc aucun couple de solution possible
x/3 - y/4 = 3 - y
x/2 + 3y/6 = 1/3
4x - 3y = 12(3 - y)
3x + 3y = 6 * 1/3
4x - 3y = 36 - 12y
3x + 3y = 2
4x - 3y + 12y = 36
3x + 3y = 2
(1) 4x + 9y = 36
(2) 3x + 3y = 2 (on multiplie par -3)
(1) 4x + 9y = 36
(3) -9x - 9y = -6
On additionne (1) et (3) :
4x + 9y - 9x - 9y = 36 - 6
-5x = 30
x = -30/5
x = -6
On remplace x dans (2) :
3x + 3y = 2
3 * (-6) + 3y = 2
-18 + 3y = 2
3y = 2 + 18
y = 20/3
S = (-6 ; 20/3)
