You have the following system of equations:
3x - 3y + 3z = 0 (1)
2x - y - 3z = 2 (2)
-7x + 6y - 2z = -2 (3)
In order to determine if the previous system has solution or not, proceed as follow:
Add equation (1) and (2):
3x - 3y + 3z = 0
2x - y - 3z = 2
5x - 4y = 2 (5)
Multiply the equation (3) by -3 and the equation (2) by 2:
(-7x + 6y - 2z = -2)(-3)
21x - 18y + 6z = 6
(2x - y - 3z = 2)(2)
4x -2y - 6z = 4
Add the previous results:
21x - 18y + 6z = 6
4x -2y -6z = 4
25x - 20y = 10 (6)
You can notice that equation (6) is five times equation (5). It means that there is no way of getting a solution for x or y with equations (5) and (6).
the previous situation also means that there is no solution to the system of equations.