12x + 4y = 16
 9x + 3y = 15

You don't add the like terms together until
you have multiplied them through by whatever
you need to multiply them by so that when you
add the like terms together, one of the letters
x or y, will cancel out.

To make the y terms cancel out:
1.  Find the least common multiple of the coefficients
    of y.  They are 4 and 3 and their least common
    multiple is 4×3 or 12.

2. Multiply the first equation though by 3 to make the 
   4y into a 12y, like this:

   36x + 12y = 48

3. Multiply the second equation through by -4 to make 
   the 3y into a -12y so it will cancel with the 12y
   when we add like terms:

   9x +  3y =  15
 -36x - 12y = -60 

4. Add the like terms:

   36x + 12y =  48
  -36x - 12y = -60
------------------
    0x +  0y = -12
           0 = -12

That is false so the system is inconsistent and there
are no solutions. So the lines do not cross so they
are parallel.  

Edwin