Answer
$(\frac{4-4t}{3}, \frac{5t-2}{3}, t)$
Work Step by Step
Step 1. Set up the augmented matrix of the system of equations:
$\begin{array} \\A=\\ \end{array}
\begin{bmatrix} 1&-1&3&2\\ 2&1&1&2\\ 3&0&4&4 \end{bmatrix}
\begin{array} \\ \\R_2-2R_1\to R_2\\R_3-3R_1\to R_3\\ \end{array}$
Step 2. Do the row operations indicated on the right side of the matrix:
$\begin{array} \\A=\\ \end{array}
\begin{bmatrix} 1&-1&3&2\\ 0&3&-5&-2\\ 0&3&-5&-2 \end{bmatrix}
\begin{array} \\ \\ \\ \\ \end{array}$
Step 3. The last two rows are the same. Let $z=t$, we have $3y-5t=-2$ or $y=\frac{5t-2}{3}$. Use row-1 to get $x-\frac{5t-2}{3}+3t=2$ or $x=\frac{4-4t}{3}$
Step 4. Conclusion: the solutions are $(\frac{4-4t}{3}, \frac{5t-2}{3}, t)$
