Answer
neither
Work Step by Step
Using $y=mx+b$ where $m$ is the slope, the slope of the first equation,
\begin{array}{l}\require{cancel}
2x+3y=1
\\\\
3y=-2x+1
\\\\
y=-\dfrac{2}{3}x+\dfrac{1}{3}
\end{array}
is $m_1=
-\dfrac{2}{3}
.$
Using $y=mx+b$ where $m$ is the slope, the slope of the second equation,
\begin{array}{l}\require{cancel}
2x-3y=5
\\\\
-3y=-2x+5
\\\\
y=\dfrac{-2}{-3}x+\dfrac{5}{-3}
\\\\
y=\dfrac{2}{3}x-\dfrac{5}{3}
\end{array}
is $m_2=
\dfrac{2}{3}
.$
Since $m_1\ne m_2$ nor $m_1\cdot m_2\ne-1,$ then the given lines are $\text{
neither
}$ parallel nor perpendicular.
