Find the solution to the system of equations:
{x2y+z=2y+2z=2x+y+3z=4\displaystyle {\left\lbrace\begin{array}{c} {x}-{2}{y}+{z}=-{2}\\{y}+{2}{z}=-{2}\\{x}+{y}+{3}{z}=-{4}\end{array}\right.}



x=\displaystyle {x}=  
y=\displaystyle {y}=  
z=\displaystyle {z}=