Answer
The system is inconsistent.
Work Step by Step
$\left\{\begin{array}{lllll}
3x & -2y & +2z & =6 & \\
7x & -3y & +2z & =-1 & /R_{2}=r_{2}-r_{1}\\
2x & -3y & +4z & =0 & /R_{3}=r_{3}-2r_{1}
\end{array}\right.$
... Eliminate $z$ in eq. 2 and 3
$\left\{\begin{array}{lllll}
3x & -2y & +2z & =6 & \\
4x & -y & & =-7 & \\
-4x & +y & & =-12 & /R_{3}=r_{3}+r_{2}
\end{array}\right.$
... Eliminate y in equation 3
$\left\{\begin{array}{lllll}
3x & -2y & +2z & =6 & \\
4x & -y & & =-7 & \\
& & 0 & =-19 &
\end{array}\right.$
The third equation is impossible - there are no solutions.
The system is inconsistent.