Given the system of linear equations: {3x+y=173y+z=213z+x=18\begin{cases} 3x + y = 17 \\ 3y + z = 21 \\ 3z + x = 18 \end{cases}⎩⎨⎧3x+y=173y+z=213z+x=18 Determine the value of x+y+zx + y + zx+y+z.
141414
121212
161616
151515