Answer
$a.\quad \left\{\begin{array}{l}
y=3,\\
z=-1
\end{array}\right.$
$b.\quad \left\{\begin{array}{l}
x=1,\\
z=-1
\end{array}\right.$
$\mathrm{c}.\quad \left\{\begin{array}{l}
x=1,\\
y=3
\end{array}\right.$
Work Step by Step
$a.\quad $
The x-axis is the intersection of the xz and xy-planes, $\left\{\begin{array}{l}
y=0,\\
z=0
\end{array}\right.$
Planes $\left\{\begin{array}{l}
y=3,\\
z=-1
\end{array}\right. \quad $
intersect in a line parallel to the x-axis, and the points on this line are $(t,3,-1)$, so the given point is also on this line.
$b.\quad $
The y-axis is the intersection of the yz and xy-planes, $\left\{\begin{array}{l}
x=0,\\
z=0
\end{array}\right.$
Planes $\left\{\begin{array}{l}
x=1,\\
z=-1
\end{array}\right. \quad $
intersect in a line parallel to the x-axis, and the points on this line are $(1,t,-1)$, so the given point is also on this line.
$\mathrm{c}.\quad $
The z-axis is the intersection of the yz and xz-planes, $\left\{\begin{array}{l}
x=0,\\
y=0
\end{array}\right.$
Planes $\left\{\begin{array}{l}
x=1,\\
y=3
\end{array}\right. \quad $
intersect in a line parallel to the x-axis, and the points on this line are $(1,3,t)$, so the given point is also on this line.
