What is the solution of the following system 3x+3y=10 -9x-9y=-30

Let's divide the 2nd equation by 3:  We get -3x - 3y = -10.
If we add this result to the 1st equation, we get 0x + 0y = 0, which has infinitelyl many solutions.

Alternatively, mult. all three terms of 3x + 3y = 10 by 3, to obtain 9x + 9y = 30.
Add this result to the 2nd equation.  We get 0x + 0y = 0, which (again) is always true for all x and y values.  This system does not have a unique solution.