Write a vector equation

\left[\Rule{0pt}{3.6em}{0pt}\right. \left]\Rule{0pt}{3.6em}{0pt}\right. x +
\left[\Rule{0pt}{3.6em}{0pt}\right. \left]\Rule{0pt}{3.6em}{0pt}\right. y +
\left[\Rule{0pt}{3.6em}{0pt}\right. \left]\Rule{0pt}{3.6em}{0pt}\right. z =
\left[\Rule{0pt}{3.6em}{0pt}\right. \left]\Rule{0pt}{3.6em}{0pt}\right.

that is equivalent to the system of equations:

\left\lbrace
\begin{array}{rcl}
y-6x-6z & = & 5, \\
9x+y-5z & = & 4, \\
2y-2x-2z & = & 4.
\end{array}
\right.

that is equivalent to the system of equations:

You can earn partial credit on this problem.