Final answer:
The graphs of the given pair of equations are parallel.
Step-by-step explanation:
The given pair of equations are:
2x + 7y = -35
4x + 14y = -42
To determine whether the graphs of these equations are parallel, perpendicular, or neither, we need to compare their slopes. The slope of a line is found by dividing the coefficient of x by the coefficient of y in the linear equation.
The first equation can be rearranged as:
y = -(2/7)x - 5
The slope of the first equation is -2/7.
The second equation can be rearranged as:
y = -(4/14)x - 3
The slope of the second equation is -4/14, which simplifies to -2/7.
Since the slopes of both equations are equal (-2/7), the graphs of these equations are parallel.