Sorry that's wrong.

I think you are trying to do it my substitution.  But the
substitution method is best only when there is a term in x
or y that has a coefficient of either 1 or -1.  This is not
the case in this system.  So the best method here is the
elimination method, sometimes called the addition method.

Add the equations just as they are and the y-terms will cancel:

 5x + 3y =  -9
 5x - 3y = -51
--------------
10x      = -60

Divide both sides by 10

      = 
       x =  -6

Multiply the second equation by -1

 5x + 3y =  -9
-5x + 3y =  51
--------------
  
and add these term-by-term

 5x + 3y =  -9
-5x + 3y =  51
--------------
      6y =  42
       = 
       y = 7

Solution (x,y) = (-6,7)

Edwin