Answer
These two lines are $\textbf{parallel}$
Work Step by Step
$2x-3y=10$ $;$ $3y-2x-7=0$
Solve $2x-3y=10$ for $y$:
$2x-3y=10$
$3y=2x-10$
$y=\dfrac{2}{3}x-\dfrac{10}{3}$
Solve $3y-2x-7=0$ for $y$:
$3y-2x-7=0$
$3y=2x+7$
$y=\dfrac{2}{3}x+\dfrac{7}{3}$
Both equations are now in slope-intercept form, which is $y=mx+b$, where $m$ is the slope of the line and $b$ is its $y$-intercept.
From the equations, it can be identified that both slopes are $m=\dfrac{2}{3}$
Since the slopes of both lines are equal, these two lines are $\textbf{parallel}$
