Depending on the actual equations:
(A) If they correspond to two lines with different slopes (so they intersect), the system of equations will have ONE solution which is given by the x and the y values of the point at which they intersect.
(B) If they correspond to two lines with the SAME slope and DIFFERENT y-intercept, they are "parallel" lines and therefore will never intersect, given NO SOLUTION to the system.
(C) If they correspond to two lines with the SAME slope and SAME y-intercept as well, they are in act the very SAME eq1uation, so they overlap, and such gives you an infinite number of solutions that correspond to all the (x,y) pairs that are part of the line.
But again, if you give me the specific system of equations, we can work on their particullars and submit a precise answer.