Infinitely many solutions means u have coincident lines...the same line
3(x + 5) = 3x + 15...this produces infinitely many solutions because it is the same line.
4x + 3 = 2x + 2x + 3....infinitely many solutions
5x - 1 = 10x - 5x - 1....infinitely many solutions
I gave u a few examples :)