Answer
The two lines are perpendicular.
Work Step by Step
Solving both equations for y (rewriting in slope-intercept form) we find the slopes:
$\left[\begin{array}{lllll}
Ax+By=C_{1} & & ... & Bx-Ay=C_{2} & \\
By=-Ax+C_{1} & & & -Ay=-Bx=C_{2} & \\
y=-\frac{A}{B}x+\frac{C_{1}}{B} & & & y=\frac{B}{A}x-\frac{C_{2}}{A} & \\
& & & & \\
m_{1}=-\frac{A}{B} & & & m_{2}=\frac{B}{A} &
\end{array}\right]$
Both slopes are defined, as $A\neq 0$ and $B\neq 0$, and we note that
$m_{1}\cdot m_{2}=-1$,
meaning that the two lines are perpendicular.
