Answer
$(7t-5,8t-4,t)$
Work Step by Step
Step 1. Establish the augmented matrix of the system and use the Gauss Eliminations method:
$\begin{vmatrix} -4 & -1 & 36 & 24 \\ 1 & -2 & 9 & 3\\-2 & 1 & 6 & 6 \end{vmatrix} \begin{array}(R_2\leftrightarrow R_1 \\.\\.\\ \end{array}$
Step 2. exchange row2 with row 1:
$\begin{vmatrix} 1 & -2 & 9 & 3 \\ -4 & -1 & 36 & 24\\-2 & 1 & 6 & 6 \end{vmatrix} \begin{array} . \\R_2+4R_1\to R_2\\R_3+2R_1\to R_3\end{array}$
Step 3. Do the operations given on the right side of the matrix.
$\begin{vmatrix} 1 & -2 & 9 & 3 \\ 0 & -9 & 72 & 36\\0 & -3 & 24 & 12 \end{vmatrix} \begin{array} . \\R_2/(-9)\to R_2\\R_3/(-3)\to R_3\end{array}$
Step 4. Simplify the second and third rows:
$\begin{vmatrix} 1 & -2 & 9 & 3 \\ 0 & 1 & -8 & -4\\0 & 1 & -8 & -4 \end{vmatrix}$
Step 5. 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 4 as:
$\begin{cases} x-2y+9t=3 \\ y-8t=-4 \end{cases} $
which gives the solutions as $x=7t-5,y=8t-4,z=t$