Question

12. Working over \( \mathbb{R} \), find a parametric solution to the following system of equations: \[ \begin{array}{r} x+y+3 z=4 \\ -x+y+z=0 \\ -x+5 y+9 z=8 \end{array} \] \[ (x, y, z)=(2+t, 2-2 t, t), \quad t \in \mathbb{R} \] \[ (x, y, z)=(2+2 t, 2-t, t), \quad t \in \mathbb{R} \] \[ (x, y, z)=(2-t, 2+2 t, t), \quad t \in \mathbb{R} \] \[ (x, y, z)=(2-t, 2-t, t), \quad t \in \mathbb{R} \] \[ (x, y, z)=(2-t, 2-2 t, t), \quad t \in \mathbb{R} \]

          12. Working over \( \mathbb{R} \), find a parametric solution to the following system of equations:
\[
\begin{array}{r}
x+y+3 z=4 \\
-x+y+z=0 \\
-x+5 y+9 z=8
\end{array}
\]
\[
(x, y, z)=(2+t, 2-2 t, t), \quad t \in \mathbb{R}
\]
\[
(x, y, z)=(2+2 t, 2-t, t), \quad t \in \mathbb{R}
\]
\[
(x, y, z)=(2-t, 2+2 t, t), \quad t \in \mathbb{R}
\]
\[
(x, y, z)=(2-t, 2-t, t), \quad t \in \mathbb{R}
\]
\[
(x, y, z)=(2-t, 2-2 t, t), \quad t \in \mathbb{R}
\]