How many solutions does a system of equations have that are lines that are parallel?

To answer this question, you have to ask yourself, "What specifically is a solution to a system of equations?"

The answer to this question is: A solution is where the two lines intersect each other.

Now, you have to think, "Where do these two lines intersect each other?"

Well, one big factor is knowing that both of these lines are parallel to each other. That means they run alongside each other and never cross over.

If you put piece by piece together with this information, you can deduce that two parallel linear lines will never cross over each other and thus, have no solutions to them.