Answer
$(5-t, -3+5t, t)$
Work Step by Step
Step 1. Establish the augmented matrix of the system and use the Gauss Eliminations method:
$\begin{vmatrix} 1 & -1 & 6 & 8 \\ 1 & 0 & 1 & 5\\1 & 3 & -14 & -4 \end{vmatrix} \begin{array}(.\\R_2-R1\to R_2\\R3-R1\to R3\\ \end{array}$
Step 2. Do the operations given on the right side of the matrix.
$\begin{vmatrix} 1 & -1 & 6 & 8 \\ 0 & 1 & -5 & -3\\0 & 4 & -20 & -12 \end{vmatrix} \begin{array}(.\\.\\R3/4\to R3\\ \end{array}$
Step 3. Simplify the second and third rows:
$\begin{vmatrix} 1 & -1 & 6 & 8 \\ 0 & 1 & -5 & -3\\0 & 1 & -5 & -3 \end{vmatrix} \begin{array}(.\\\\\\ \end{array}$
Step 4. Because the third row is the same as the second, we have dependent equations and unlimited solutions.
Let $z=t$ and write the equations from step 3 as:
$\begin{cases} x-2+6t=8 \\ y-5t=-3 \end{cases} $
which gives the solutions as $x=5-t,y=-3+5t,z=t$
