Answer :
x - 7y = 10
-7y = -x + 10
y = 1/7x - 10/7....slope here is 1/7, y int = -10/7
2x + 4y = 21
4y = -2x + 21
y = -1/2x + 21/4...slope is -1/2, y int = 21/4
neither <==
for them to be parallel, they would need the same slope
for them to be perpendicular, they would need negative reciprocal slopes
they have neither
-7y = -x + 10
y = 1/7x - 10/7....slope here is 1/7, y int = -10/7
2x + 4y = 21
4y = -2x + 21
y = -1/2x + 21/4...slope is -1/2, y int = 21/4
neither <==
for them to be parallel, they would need the same slope
for them to be perpendicular, they would need negative reciprocal slopes
they have neither
To decide, you would better find their slopes
x - 7y = 10
-7y = 10-x
y = 1/7 x -10/7
the slope = 1/7
2x +14y = 21
14y = 21 - 2x
y = 21/14 - 2/14 x
y = -1/7 x + 3/2
the slope = -1/7
For our case, they are not parallel nor perpendicular
x - 7y = 10
-7y = 10-x
y = 1/7 x -10/7
the slope = 1/7
2x +14y = 21
14y = 21 - 2x
y = 21/14 - 2/14 x
y = -1/7 x + 3/2
the slope = -1/7
For parallel lines:
"All parallel lines have the same slope!"
--------------
For perpendicular
lines:
"Their slopes' product is -1"
For our case, they are not parallel nor perpendicular