How many solutions does the system 2y=10x-14 and 5x-y=7 have ?

I find it of tremendous use to convert to the slope intercept form to easily visualize the lines.  The first is:
y = 5x - 7  [Dividing both sides by 2] and the second is:
-y = -5x + 7  [Subtracting 5x from each side]
y = 5x - 7 [Dividing each side by -1]

These two equations represent the same line.  If the lines were parallel, there would be no solution.  If the lines intersected, there would be only one unique solution satisfying both equations (the point of intersection).

In this case, where the two equations represent the same line, the number of solutions is infinite.

The answer is:  ∞