If the system of linear equations.
\[
\begin{array}{l}
8 x+y+4 z=-2 \\
x+y+z=0 \\
\lambda x-3 y=... VIDEO
If the system of linear equations.
\[
\begin{array}{l}
8 x+y+4 z=-2 \\
x+y+z=0 \\
\lambda x-3 y=\mu
\end{array}
\]
has infinitely many solutions, then the distance of the point \( \left(\lambda, \mu,-\frac{1}{2}\right) \) from the plane \( 8 x+y+4 z+2=0 \)
(a) \( 3 \sqrt{5} \)
(b) 4
(c) \( \frac{26}{9} \)
(d) \( \frac{10}{3} \)
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