We will use an example to answer this question. Let's consider a system of linear equations. Note that both the and the variables have the same coefficient in both equations. Thus, in order to use the elimination method, we will subtract Equation (II) from Equation (I). We arrived to a true statement. Its truthfulness does not depend on any variable. Thus, any value for and will satisfy the statement. This happens when the two lines are coincidental and then the system has infinitely many solutions.
Finally, to answer this question, we will use a third example. In this example the and the variables have opposite coefficients. Therefore, to solve the system, we will add the equations. Since we know that we have a arrived at a false statement. There are no values for and that satisfy it. Thus, the system has no solution. This means the lines do not intersect. Every time we arrive to a false statement, the system has no solution.