Question

Resolva os sistemas a seguir:

Answer 1

c) podemos multiplicar por -1 a primeira linha para anular x e y, achando o valor de z
-3x+2y-z=-2
-4y+3z=-2
3x+2y=36/15
__________
0x+0y+2z=-2-2+36/15
2z=-30/15-30/15+36/15
2z=-24/15
z=-12/15=-4/5
substituindo z
-4y+3(-4/5)=-2
-4y-12/5=-2
-4y=-10/5+12/5
-4y=2/5
4y=2/5
y=1/10
substituindo o y
3x+2(1/10)=36/15
3x+2/10=36/15
3x=36/15-3/15
3x=33/15
3x=11/15

d) agr por substituição
x+y+z+t=2
x=-y-z-t+2

x+2y-t=4
(-y-z-t+2)+2y-t=4
y=z+2t+2

x=-(z+2t+2)-z-t+2
x=-2z-3t

2x-y+z-t=-3
2(-2z-3t)-(z+2t+2)+z-t=-3
-4z-6t-z-2t-2+z-t=-3
-4z-9t=-9
t=1-4z/9

x=-2z-3(1-4z/9)
x=-6z/3-3+4z/3
x=-2z/3-3
y=z+2(1-4z/9)+2
y=z+2-8z/9+2
y=z/9+4
falta achar o z