The solution to the system of equations is:

$x = -2, \quad y = -6, \quad z = -3$

Would you like more details or have any questions?

Here are some related questions for further practice:

1. What is the method used to solve a system of equations like this?
2. How can you check if the solution satisfies all three equations?
3. How would the solution change if one of the constants (e.g., 4 in the first equation) were different?
4. Can you solve the system graphically?
5. What happens if the system of equations has no solutions or infinite solutions?

Tip: Always substitute the solution back into the original equations to verify its correctness!