Answer
The lines are parallel to each other.
Work Step by Step
RECALL:
(1) Parallel lines have the same slope.
(2) Perpendicular lines have slopes whose product is $-1$ (negative reciprocals of each other).
(3) The slope-intercept form of a line's equation is $y=mx + b$ where $m$=slope and $(0, b)$ is the line's y-intercept.
Write both equations in slope-intercept form to obtain:
First Equation:
$3x-5=7y
\\\frac{3x-5}{7}=\frac{7y}{7}
\\\frac{3}{7}x-\frac{5}{7}=y
\\y=\frac{3}{7}x-\frac{5}{7}$
The slope of this line is $\frac{3}{7}$.
Second Equation:
$7y-3x=7
\\7y-3x+3x=7+3x
\\7y=7+3x
\\7y=3x+7
\\\frac{7y}{7}=\frac{3x+7}{7}
\\y=\frac{3}{7}x+1$
The slope of this line is $\frac{3}{7}$.
Since the two lines have the same slope, then they are parallel to each other.
