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
Thats the first equation. But when you unravel it like this, you find that
its exactly the same as the second equation. Both of them represent
the same straight line on a graph. If you graphed both of them, youd
only see one line !
The solution of a pair of equations is the point on a graph where their
lines cross. Theres 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.