Solve the system of equations. Your answers must be fractions (decimals are not allowed). $$\left\lbrace \begin{array}{rcr} x_{1}-2x_{2}-2x_{3} & = & 2 \\ 3x_{1}+3x_{2}-x_{3} & = & 2 \\ 2x_{1}+x_{2}+3x_{3} & = & -1 \end{array} \right.$$
$\vec{x} =$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$.