Question

How do you know when there are no solutions to a system of equations?

How do you know there are infinity many solutions to a system of equations?

How do you know when there is one solution to system of equations?

Answer 1

No solution
========
The lines are parallel
eg
y = 2x + 3; y = 2x + 5

Infinite solutions
============
When one equation reduces to the second one.
2y = 10x + 6
y = 5x + 3 When you divide the first one by 2, you get the second one.