Question

Systems of equations with the same slopes have infinitely many solutions.

Always

Sometimes

Never

Answer 1

for infinitely many solutions to exist, the equations must be the same thing. If one equation is ax + by +c = 0 and the other is k(ax+by+c) = 0 i.e. each term is multiplied by a fixed non-zero constant, then the two equations are the same, and there exist infinite values of x,y that satisfy both equations.

However, if only the slope is same but the y-intercept is different, then clearly both lines are non-intersecting parallel lines. These will never meet and thus have no possible solution.
So, your answer would be 'sometimes'