solving a system of linear equations

Solve the system of linear equations and interpret your solution geometrically:

[1] 2x + y + 2z - 4 = 0

[2] x - y - z - 2 = 0

[3] x + 2y - 6z - 12 = 0

I keep getting really odd numbers with a lot of fractions whenever i try to solve for it.

First i eliminated x

[1] 2x+y+2z-4=0 [2] x-y-z-2=0

[2] - __2x-2y-2z-4=0 __ [3] - __x=2y-6z-12=0__

[4] 3y+4z=0 [5] -3y+5z+10=0

then i eliminated y to solve for z

[4] 3y+4z=0

[5] + __-3y+5z+10 = 0 __

9z+10=0

z=-10/9

then i solved for y

[4]3y+4(-10/9)=0

y=1.48

then i solved for x

[1]2x+1.48+2(-10/9)=0

x= 0.371

so im guessing this means my point of intersection (0.371,1.48, -1.11)

im not sure if this is correct or if i missed anything, if anyone can give me their input i would really appreciate it. I'm not sure how to interpret it geometrically either.