Question

5x +y =6
4x +5y=2
which one is parallel, perpendicular or are neither

Answer 1

re-write equations as:
y=-5x+6
y==x*4/5 + 1/2
compare numbers in a front of x... neiher

Answer 2

both equations are written in Standard Form: Ax + By = C
the A for the first equation is 5 and the B is 1, so A/B = 5/1
the A for the 2nd equation is 4 and the B is 5, so A/B = 4/5

if A/B for both are the same, the lines are parallel.

if the A/B for both multiply to make -1, they are perpendicular

if neither is true, then the lines intersect and they are neither par or perp.

check with your teacher, s/he might want you to solve for y like the above post mentions. But use my rule with the above post.