= Solution
The <linear system> has the <matrix> form
$$
\boxed{A\boldsymbol x=\boldsymbol b,\qquad
A=\begin{pmatrix}0&-3&-2\\1&-4&-2\\-3&4&1\end{pmatrix},\quad
\boldsymbol x=\begin{pmatrix}x_1\\x_2\\x_3\end{pmatrix},\quad
\boldsymbol b=\begin{pmatrix}4\\2\\-1\end{pmatrix}.}
$$
The first equation gives $3x_2+2x_3=-4$. Substitute it into the second to obtain $x_1=2+4x_2+2x_3=x_2-2$. Substitution into the third gives $x_2+x_3=-7$. Consequently
$$
3x_2+2(-7-x_2)=-4\quad\Longrightarrow\quad x_2=10.
$$
It follows that
$$
\boxed{\boldsymbol x=(8,10,-17)^T.}
$$
Substitution verifies all three equations. Also $\det A=1\ne0$, so this <solution of a linear system> is unique.
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