Answer
The linear system of equations is:
\[\begin{align}
& y=\frac{1}{3}x+2 \\
& y=\frac{1}{3}x-2
\end{align}\]
Work Step by Step
Since the solution set is\[\varnothing \], it implies the two equations does not intersect at all.
According to the given graph the equations that does not intersect are,
\[\begin{align}
& x-3y=-6 \\
& x-3y=6
\end{align}\]
Solve the above equations to verify.
Subtract the two equations as follows:
\[\underline{\begin{align}
& x-3y=-6 \\
& -x+3y=-6
\end{align}}\]
\[\ \ \ \ \ \ \ \ 0\ne -12\]
Since, \[0\ne -12\] it implies that the system has no solution and the solution set is\[\varnothing \]
Hence, the linear system of equations is:
\[\begin{align}
& y=\frac{1}{3}x+2 \\
& y=\frac{1}{3}x-2
\end{align}\]
With the solution set as\[\varnothing \].
