6x + 8y = 6788, and x - y must be = 510

6x + 8y   =  6788

x - y  = 510

Using the second equation,  we can rearrange it as  :  x - 510  = y

And substituting for y in the first equation, we have

6x + 8 [ x - 510]  = 6788   simplify

6x + 8x - 4080   = 6788 

14x - 4080  = 6788       add 6788 to each side

14x  = 10868        divide both sides by 14

x  =  5434/7

And y = 5434/7 - 510  =  [5434 - 3570] / 7  =  1864 / 7