Answer
$x= \frac{3}{2}-2t$
$y=1+2t$
$z=t$
Work Step by Step
Write the augmented matrix of the system of linear equations.
$ \begin{bmatrix}
2 & 1 & 2 & 4\\
2 & 2 &0 & 5\\
2 & -1 & 6 & 2
\end{bmatrix} $
Divide the first row by 2.
$ \begin{bmatrix}
1 & \frac{1}{2} & 1 & 2\\
2 & 2 &0 & 5\\
2 & -1 & 6 & 2
\end{bmatrix} $
Add -2 times the 1st row to the 2nd row to produce a new 2nd row.
Add -2 times the 1st row to the 3rd row to produce a new 3rd row.
$ \begin{bmatrix}
1 & \frac{1}{2} & 1 & 2\\
0 & 1 &-2 & 1\\
0 & -2 & 4 & -2
\end{bmatrix} $
Add 2 times the 2nd row to the 3rd row to produce a new 3rd row.
$ \begin{bmatrix}
1 & \frac{1}{2} & 1 & 2\\
0 & 1 &-2 & 1\\
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.
$z=t$
$y=1+2t$
$x= \frac{3}{2}-2t$
