Answer
no solution.
Work Step by Step
Step 1. Set up the augmented matrix of the system of equations:
$\begin{array} \\A=\\ \end{array}
\begin{bmatrix} 1&-2&3&1\\ 2&-1&1&3\\ 2&-7&11&2\\ \end{bmatrix}
\begin{array} \\ \\R_2-2R_1\to R_2\\R_3-2R_1\to R_3 \end{array}$
Step 2. Do the row operations indicated on the right side of the matrix:
$\begin{array} \\A=\\ \end{array}
\begin{bmatrix} 1&-2&3&1\\ 0&3&-5&1\\ 0&-3&5&0\\ \end{bmatrix}$
Step 3. Add up the last two rows to get $0=1$ indicating that there is no solution to the system.
