Question 550370
Solve using the elimination method rather than guessing: First elimination one variable, then another

x + y + z = 6
plus
-x + y + 3z = 10
2y+4z=16


2x - y + 2z = 6
plus 2 times
-x + y + 3z = 10
-2x+2y+6z=20
which gives
y+5z=26
We already had:
2y+4z=16
multiply y+5z=26 by -2
-2y-10z=-52
-6z=-36
z=6

Now that we know z=6 sub it in 2y+4z=16 
2y+24=16
2y=-8
y=-4

x + y + z = 6

x+-4+6=6
x=4

(4,-4,6)