Remember, you can solve systems of equations with elimination or substitution when solving algebraically.
Elimination is best when two of the same variables have the same or opposite coefficients, so can easily cancel out.
Substitution is best when a variable is already by itself, or would be easy to get by itself.
If you get that two numbers are equal, and no variables are left, you have infinitely many solutions! The two lines are the exact same line.
If you get that two numbers are equal, but they are not really (like 2 = 4), then you have no solutions! The two lines are parallel.