Question

The graph of a system of equations will intersect at exactly 1 point.

Always
Sometimes
Never

Answer 1

if they have a solution

Answer 2

If the equations are linear, they could be parallel lines, which will intersect at zero points.
If the equations are linear and non-parallel, they will intersect at one point.
If the equations are non-linear, they could intersect at more than one point.

So, sometimes.