How do you know when an equaton has an infinite number of solutions?

How do you know when an equation has no solution?

If you can break an equation into two equations, and you can plot those two equations on graph (or at least visualise the graphs), then it becomes very easy.

You will have no solutions if the two graphs don't meet at all.
You will have infinite solutions if the graphs are the same, or overlap for some range or for infinity.

I don't know if that's how it should be explained though... but that's how I go about it. :)

By just looking at the equation, we can tell if it has infinite solutions or not by noting if there are more variables than there are equations.

Take 5x+3y=10

This has infinite solutions because there are two variables but only one equation.