Question

Resolva o sistema:

x+y+2z=1
x+2y+3y=2
2x-y+z=2

Qual o Cálculo?

Answer 1

x+y+2z=1
x+2y+3y=2
2x-y+z=2

x+y+2z=1
x=1-y-2z

x+2y+3y=2
1-y-2z+2y+3y=2
4y-2z=1

2x-y+z=2
2.(1-y-2z)-y+z=2
2-2y-4z-y+z=2
-3y-3z=0

4y-2z=1
-3y-3z=0
y-5z=1
y=1+5z

4y-2z=1
4(1+5z)-2z=1
4+20z-2z=1
18z=1-4
18z=-3
z=-3/18=-1/6

y=1+5z
y=1+5.(-1/6)
y=1-5/6
y=6-5
y=1

x=1-y-2z
x=1-1-2.(-1/6)
x=2/6=1/3

x=1/3, y=1 e z=-1/6

Espero ter ajudado!