#### Answer

$y=\displaystyle \frac{1}{3}x-2$
$y=\displaystyle \frac{1}{3}x+2$

#### Work Step by Step

A graphical solution to a system of linear equations is a point of intersection of two lines.
If the solution set is empty, the lines do not intersect. They are parallel.
From the graph, the pair of parallel lines have equations
$ x-3y=6\qquad$and$\quad x+3y=-6$
Slope-intercept form: solve each equation for $y$:
$\left[\begin{array}{lll}
x-3y=6 & & x+3y=-6\\
-3y=-x+6 & & -3y=-x-6\\
y=\frac{1}{3}x-2 & & y=\frac{1}{3}x+2
\end{array}\right]$
The system:
$y=\displaystyle \frac{1}{3}x-2$
$y=\displaystyle \frac{1}{3}x+2$