Call equations A, B and C.
A+C: -6z=-18, so 6z=18 and z=3.
B+C: 5x+3z=-1. Substitute z=3: 5x+9=-1, 5x=-10, x=-2.
Substitute x=-2 and z=3 in A: 2-5y-15=2, -5y-13=2, -5y=15, y=-3.
Solution: x=-2, y=-3, z=3.
Check solution: 2+15-15=2; -8+15+12=19; -2-15-3=-20.
All equations check out when substitutions are made for x, y and z.