Answer
The lines are neither parallel nor perpendicular.
Work Step by Step
We have the equations
$$2x -3y= 6, \ \
3x + 5y = 7$$
We write the equations in slope-intercept form $y=mx+b$ as follows:
$$ y=\frac{2}{3}x-2, \quad y=-\frac{3}{5}x+\frac{7}{5} .$$ We note that the slopes $m_1=\frac{2}{3}$ and $m_2=-\frac{3}{5}$ do not satisfy the condition of being parallel ($m_1\ne m_2$). They are also not perpendicular because $m_1*m_2=\frac{2}{3}\times\frac{-3}{5}=\frac{-6}{15}\ne -1$. See the figure below.
