Solve system of equation by using elimination.

3x+y+2z=1

2x-y+z=-3

x+y-4z=-3

You have to combine 2 different sets of the 3 equations using elimination, then you are left with 2 equations with 2 variables.

3x+y+2z=1

+2x-y+z=-3

5x+0y+3z=-2

2x-y+z=-3

+x+y-4z=-3

3x+0y-3z=-6

Then you solve them and plug them into one of the original equations to get the third variable.

5x+3z=-2 - - > 3z=-5x-2 - - > z=-5/3x-2/3

3x-3z=-6 - - > - 3z=-3x-6 - - > z=x+2

x+2=-5/3x-2/3

8/3x=8/3

x=1

z = (1) + 2

Z=3

3x+y+2z=1

3 (1) + y+2 (3) = 1

3+y+6=1

y=-8

The final answer is then (1, - 8, 3), for (x, y, z).

I hope this made some sense.