Answer
Inconsistent system
Work Step by Step
Build the augmented matrix of the system of equations;
$\begin{bmatrix}2&-3&1&|&1\\1&-2&3&|&2\\3&-4&-1&|&1\end{bmatrix}$
Bring the matrix to the row reduced echelon form:
Add $-R_2$ to $R_1$:
$\begin{bmatrix}1&-1&-2&|&-1\\1&-2&3&|&2\\3&-4&-1&|&1\end{bmatrix}$
Add $-R_1$ to $R_2$:
$\begin{bmatrix}1&-1&-2&|&-1\\0&-1&5&|&3\\3&-4&-1&|&1\end{bmatrix}$
Add $-3R_1$ to $R_3$:
$\begin{bmatrix}1&-1&-2&|&-1\\0&-1&5&|&3\\0&-1&5&|&4\end{bmatrix}$
Add $-R_2$ to $R_1$ and $R_3$:
$\begin{bmatrix}1&0&-7&|&-4\\0&-1&5&|&3\\0&0&0&|&1\end{bmatrix}$
The last row shows that the system is inconsistent, therefore it has no solution.
