System of linear equations

I've worked through this one, but I must be doing something wrong because my answer is not coming out correctly. I need to solve this system of linear equations and will be using the addition method to eliminate one of the variables:

$\displaystyle y=-\frac{2}{3}x-3$

$\displaystyle x=-\frac{3}{2}y+9$

Now, I broke this down to the following, and this is where I think I am messing up. I presume I need to get 'x' and 'y' on the same left side, so I did:

$\displaystyle \frac{2}{3}x+\frac{1}{1}y=-3$

$\displaystyle \frac{1}{1}x+\frac{3}{2}y=9$

Is this correct, or am I missing something? I know in the end I should end up with a separate value for 'x' and 'y', but when I add the two equations together I end up getting something like (don't laugh) 0x+0y=54, which obviously is wrong, so I cannot finish the equation.

Your guidance is appreciated.