Answer:
x=3 ;y=4.5 ;z=-4
Step-by-step explanation:
x+2y+3z=0
2(x+2y+3z=0)
2x+4y+6z=0 [1]
2x+y+3z=0 [2]
[1] - [2]:(elimination)
(2x+4y+6z)-(2x+y+3z)=0-0
2x+4y+6z-2x-y-3z=0
3y+3z=0 [3] ×2
6y+6z=0
3x+2z=1 [4] ×3
9x+6z=3
([4]×3)-([3]×2): (elimination)
(9x+6z)-(6y+6z)=3-0
9x+6z-6y-6z=3
3x=3
x=3
Substitute x=3 into 3x+2z=1
3(3)+2z=1
9+2z=1
9-1=-2z
8=-2z
z=-4
Substitute z=-4 & x=3 into x+2y+3z=0
3+2y+3(-4)=0
3+2y-12=0
2y-9=0
2y=9
y=4.5
