Répondre :
(E1) : 2x+3y-z=-7
(E2) : x-2y+2z=11
(E3) : 5x+y+4z=15
4(E1) : 8x+12y-4z=-28
2(E2) : 2x-4y+4z=22
(E3) : 5x+y+4z=15
4(E1)+(E3) : 13x+13y=13 => 13(x+y)=13 => x+y=13/13 => x+y=1
4(E1)+2(E2) : 10x+8y=-6=> 2(5x+4y)=-6 => 5x+4y=-6/2 =>5x+4y=-3
(E1) : 2x+3y-z=-7
4(E1)+(E3) : y=1-x
4(E1)+2(E2) : 5x+4(1-x)=-3 => 5x+4-4x=-3 => 5x-4x=-3-4 => x=-7
(E1) : 2x+3y-z=-7
4(E1)+(E3) : y=1-x=1-(-7)=1+7=8
4(E1)+2(E2) : x=-7
(E1) : z=2x+3y+7=2(-7)+3(8)+7=-14+24+7=-10+7=-3
4(E1)+(E3) : y=8
4(E1)+2(E2) : x=-7
(E1) : z=-3
S=(x,y,z)=(-7,8,-3)