how many solution exist for each system of equations?



The second one is already in slope-intercept form.
We need to do a little work on the first one.

3x - 3y = -6

Subtract 3x from each side:

-3y = -3x - 6

Divide each side by -3 :

y = x + 2

That’s the first equation. But when you unravel it like this, you find that
it’s exactly the same as the second equation. Both of them represent
the same straight line on a graph.   If you graphed both of them, you’d
only see one line !

The ’solution’ of a pair of equations is the point on a graph where their
lines cross.   There’s no such point here, because each and every point
of the first equation is also a point of the second one.  

This pair (system) of equations has no solution.