First work out a determinant, by writing just the coefficients of the variables in the order x, y, z: Δ=
| 1 2 1 |
| -1 3 2 | = 1(-6+2)-2(2-0)+1(1-0)=-4-4+1=-7.
| 0 -1 -2 |
Now a determinant for each variable by replacing the variable column with the constants for each line: Δx=
| -1 2 1 |
| 2 3 2 | = -1(-6+2)-2(-4-2)+1(-2-3)=4+12-5=11.
| 1 -1 -2 |
x=Δx/Δ=-11/7.
Δy=
| 1 -1 1 |
| -1 2 2 | = 1(-4-2)+1(2-0)+1(-1-0)=-6+2-1=-5.
| 0 1 -2 |
y=Δy/Δ=5/7.
Δz=
| 1 2 -1 |
| -1 3 2 | = 1(3+2)-2(-1-0)-1(1-0)=5+2-1=6.
| 0 -1 1 |
z=Δz/Δ=-6/7.
SOLUTION: x=-11/7, y=5/7, z=-6/7.