1. Solve the system: $$\begin{cases} x + y + z = 6 \\ 2x - y + 3z = 14 \\ -x + 4y - z = 2 \end{cases}$$ 2. Solve the system: $$\begin{cases} 3x + 2y - z = 7 \\ x - y + 4z = 10 \\ 2x + 3y + z = 13 \end{cases}$$ 3. Solve the system: $$\begin{cases} 2x + y + 3z = 12 \\ 4x - 2y + z = 10 \\ -x + 3y + 2z = 7 \end{cases}$$ 4. Solve the system: $$\begin{cases} x + 2y + 3z = 14 \\ 3x - y + z = 10 \\ 2x + y - 2z = 3 \end{cases}$$ 5. Solve the system: $$\begin{cases} 4x + y - z = 9 \\ x + 3y + 2z = 16 \\ 2x - y + 3z = 11 \end{cases}$$ 6. Solve the system: $$\begin{cases} 5x - 2y + z = 8 \\ 3x + y - 4z = 1 \\ x + 4y + 2z = 15 \end{cases}$$ 7. Solve the system: $$\begin{cases} 2x + 3y - z = 7 \\ x - 4y + 2z = 1 \\ 3x + y + z = 12 \end{cases}$$ 8. Solve the system: $$\begin{cases} x + y + z = 9 \\ 2x - 3y + 4z = 13 \\ 3x + 2y - z = 10 \end{cases}$$ 9. Solve the system: $$\begin{cases} 3x + y - 2z = 4 \\ x + 4y + z = 15 \\ 2x - y + 3z = 11 \end{cases}$$ 10. Solve the system: $$\begin{cases} x - y + 2z = 5 \\ 4x + 3y - z = 14 \\ 2x + y + 3z = 13 \end{cases}$$