Answer
No solution.
Work Step by Step
Step 1. Establish the augmented matrix of the system and use the Gauss Eliminations method:
$\begin{vmatrix} 3 & 1 & 0 & 2 \\ -4 & 3 & 1 & 4\\2 & 5 & 1 & 0 \end{vmatrix} \begin{array}(R_3/2\leftrightarrow R_1 \\.\\.\\ \end{array}$
Step 2. divide row 3 by 2 and exchange it with row 1:
$\begin{vmatrix} 1 & 5/2 & 1/2 & 0 \\ -4 & 3 & 1 & 4\\3 & 1 & 0 & 2 \end{vmatrix} \begin{array} . \\R_2+4R_1\to R_2\\2(R_3-3R_1)\to R_3\end{array}$
Step 3. Do the operations given on the right side of the matrix.
$\begin{vmatrix} 1 & 5/2 & 1/2 & 0 \\ 0 & 13 & 3 & 4\\0 & -13 & -3 & 4 \end{vmatrix} \begin{array} . \\.\\R_3+R_2\to R_3\end{array}$
Step 4. Add the second and third rows:
$\begin{vmatrix} 1 & 5/2 & 1/2 & 0 \\ 0 & 13 & 3 & 4\\0 & 0 & 0 & 8 \end{vmatrix} \begin{array} . \\.\\.\end{array}$
Step 5. Because the third row gives $0=8$, this system has no solution.
