if you are talking about 2 linear equations
and

1. 1 solution: means they intersect at one point meaning that they can't be paralell meaning slopes must be different. y-intercepts are irrelevant
slopes: different
y-ints: whatver you want, doesn't matter
2. many solutions usually means they are shte same line
so their sloeps and y-intercepts are the same
slopes: same
y-ints: same
3. undefined means tehy don't intersect meaning they are paralell meaning they have same slopes but different y-intercepts
slopes: same
y-ints: different