-6x-2y+2z=-8 (a)
3x-2y-4z=8 (b)
6x-2y-6z=-18 (c)
Subtract (b) to (a)
-6x-2y+2z=-8
-
3x-2y-4z=8
___________
-9x + 6z = - 16 (d)
Subtract (b) to (c)
6x-2y-6z=-18
-
3x-2y-4z=8
___________
3x -2z = -26 (e)
Now, we have a system of 2 equations:
-9x + 6z = - 16 (d)
3x -2z = -26 (e)
Multiply (e) by 3 and add both equations, to eliminate x
-9x + 6z = - 16
+
9x - 6z = -78
___________
0 = -94
the system has no solutions