Answer
Geometrically, this means the plane that represents the solution set is translated to pass through point (-2,0,0).
Work Step by Step
$x_1+9x_2-4x_3=0$
Solving for basic variable $x_1$, we get
$x_1=-9x_2+4x_3$
$x=\begin{bmatrix}
-9x_2+4x_3\\
x_2\\
x_3
\end{bmatrix}=x_2\begin{bmatrix}
-9\\
1\\
0
\end{bmatrix}+x_3\begin{bmatrix}
4\\
0\\
1
\end{bmatrix}$
$x_1+9x_2-4x_3=-2$
Solving for basic variable $x_1$, we get
$x_1=-9x_2+4x_3-2$. This means there will be an extra vector added to the solution set above.
$x=x_2\begin{bmatrix}
-9\\
1\\
0
\end{bmatrix}+x_3\begin{bmatrix}
4\\
0\\
1
\end{bmatrix}+\begin{bmatrix}
-2\\
0\\
0
\end{bmatrix}$
Geometrically, this means the plane that represents the solution set is translated to pass through point (-2,0,0).
