Lines are parallel if their slopes are exactly the same, and perpendicular if their slopes are negative reciprocals. Any other relationship between the slopes would result in neither parallel nor perpendicular lines. Let's write both equations in slope-intercept form, highlighting their slopes.
Given Equation
Slope-intercept form
Slope
2x+7y=-35
y= -2/7x-5
m_1= -2/7
4x+14y=-42
y= -2/7x-3
m_2= -2/7
Since the lines have equal slopes, we can conclude that they are parallel.