To solve this system of equations, we can use the substitution method. First, we need to solve one of the equations for one of the variables. Let's solve the first equation for x:

3x = 11

x = 11/3

Now, we can substitute this value of x into the second equation to solve for y:

3(11/3) - 3y = -9

11 - 3y = -9

-3y = -20

y = 20/3 = 6 2/3

Now that we have values for both x and y, we can substitute them back into either equation to check our work:

3(11/3) = 11

11 = 11

and

3(11/3) - 3(6 2/3) = -9

11 - 19 2/3 = -9

-8 2/3 = -9

Both substitutions give us equations that are true, so we have found the solution to the system: x = 11/3 and y = 6 2/3.