Expanding the parentheses and combining some values:
20x+5y=-8, so 20x+5y+0z=-8,
4x-20y+12z=23,
-5z+9y=-16, so 0x+9y-5z=-16.
Let the determinant D=
| 20 5 0 |
| 4 -20 12 | = 20(100-108)-5(-20-0)+0=-160+100=-60.
| 0 9 -5 |
Determinant Dx=
| -8 5 0 |
| 23 -20 12 | = -8(100-108)-5(-115+192)+0=64-385=-321.
| -16 9 -5 |
x=Dx/D=-321/-60=5.35.
Determinant Dy=
| 20 -8 0 |
| 4 23 12 | = 20(-115+192)+8(-20-0)+0=1540-160=1380
| 0 -16 -5 |
y=Dy/D=1380/-60=-23.
Determinant Dz=
| 20 5 -8 |
| 4 -20 23 | = 20(320-207)-5(-64-0)-8(36-0)=2260+320-288=2292
| 0 9 -16 |
z=Dz/D=2292/-60=-38.2.
Solution of this system of equations: x=5.35, y=-23, z=-38.2.