Επτά Συμμετρικά Συστήματα

Να λυθούν τα συστήματα:

$$1.\{\begin{array}{l}x+2y+z=14\\ 2x+y+z=12\\ x+y+2z=18\end{array}$$ $$2.\{\begin{array}{l}x+y=7\\ y+z=-2\\ z+x=9\end{array}$$

$$3.\{\begin{array}{l}xy=6\\ yz=-2\\ zx=10\end{array}$$ $$4.\{\begin{array}{l}(x+1)(y+1)=24\\ (y+1)(z+1)=30\\ (z+1)(x+1)=20\end{array}$$ $$5.\{\begin{array}{l}xy-x-y=11\\ yz-y-z=14\\ zx-x-z=19\end{array}$$ $$6.\{\begin{array}{l}x(x+y+z)=4\\ y(x+y+z)=6\\ z(x+y+z)=54\end{array}$$ $$7.\{\begin{array}{l}x+[y]+[z]=1.1\\ [x]+y+[z]=2.2\\ [x]+[y]+z=3.3\end{array}$$