Rewrite:
x+y+2z=-2
-3x-y+2z=1
x+2y-z=-4
D (coefficient determinant)=
| 1 1 2 |
| -3 -1 2 | = 1(-3)-1(1)+2(-5)=-3-1-10=-14.
| 1 2 -1 |
Dx=
| -2 1 2 |
| 1 -1 2 | = -2(-3)-1(7)+2(-2)=6-7-4=-5 so x=-5/-14=5/14.
| -4 2 -1 |
Dy=
| 1 -2 2 |
| -3 1 2 | = 1(7)+2(1)+2(11)=7+2+22=31 so y=-31/14.
| 1 -4 -1 |
Dz=
| 1 1 -2 |
| -3 -1 1 | = 1(2)-1(11)-2(-5)=2-11+10=1 so z=-1/14.
| 1 2 -4 |
CHECK
5/14-31/14-2/14+2=-28/14=2=0 OK
-15/14+31/14-2/14-1=14/14-1=0 OK
5/14-62/14+1/14+4=-56/14+4=0 OK