Infinitely many solutions is for equal lines, no solutions is for parallel lines, and one solution is for intersecting lines.
How to identify systems of linear equations?
I assume you are asking about systems of linear equations. Where the general system of linear equations is:
y = a*x + b
y = c*x + d
There are 3 possible options for these.
"Infinitely many solutions"
This happens when both equations describe the same line, so if a = c and b = d, then there are infinite solutions.
"no solutions"
This happens when the lines are parallel lines, this happens if both lines have the same slope and different y-intercept. So this happens when a = c and b ≠ d.
"One solution"
This happens when the lines intersect at one point. The only requirement is that the slopes must be different, so a ≠ c.
If you want to learn more about systems of linear equations:
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