Answer
$x=3t+4$
$y=2t+5$
$z=t$
Work Step by Step
Write the augmented matrix of the system of linear equations.
$ \begin{bmatrix}
1 & -2 & 1& -6\\
2 & -3 & 0 & -7\\
-1 & 3& -3 & 11
\end{bmatrix} $
Add -2 times the 1st row to the 2nd row to produce a new 2nd row.
Add 1 times the 1st row to the 3rd row to produce a new 3rd row.
$ \begin{bmatrix}
1 & -2 & 1& -6\\
0 & 1 & -2 & 5\\
0 & 1& -2 & 5
\end{bmatrix} $
Add -1 times the 2nd row to the 3rd row to produce a new 3rd row.
$ \begin{bmatrix}
1 & -2 & 1& -6\\
0 & 1 & -2 & 5\\
0 & 0&0 & 0
\end{bmatrix} $
Use the parameter t to represent z(where t is any real number) and substitute further for x and y.
$z=t$
$y=2t+5$
$x=3t+4$
