Answer
$(1+s, 1+2s-t, s, t)$
Work Step by Step
Step 1. Set up the augmented matrix of the system of equations:
$\begin{array} \\A=\\ \end{array}
\begin{bmatrix} 1&-1&1&-1&0\\ 3&-1&-1&-1&2 \end{bmatrix}
\begin{array} \\ \\(R_2-3R_1)/2\to R_2\\ \end{array}$
Step 2. Do the row operations indicated on the right side of the matrix:
$\begin{array} \\A=\\ \end{array}
\begin{bmatrix} 1&-1&1&-1&0\\ 0&1&-2&1&1 \end{bmatrix}
\begin{array} \\ \\R_2-3R_1\to R_2\\ \end{array}$
Step 3. Let $w=t, z=s$, the second row gives $y-2s+t=1$ or $y=1+2s-t$, and row 1 gives $x-(1+2s-t)+s-t=0$ or $x=1+s$
Step 4. The solutions to the system are $(1+s, 1+2s-t, s, t)$
