9x-7y=-7 doesn't do anything called "come out x=1. y=16/7'.

You see, 9x-7y=-7 is ALGEBRA for this graphed line of GEOMETRY,
and the only thing that can be said about "x=1 and "y=16/7" is
that if you substitute 1 for x in 9x-7y=-7 you will get y = 16/7.

   9x - 7y = -7
 9(1) - 7y = -7
    9 - 7y = -7
   -9        -9
---------------
       -7y = -16
   
         y =  

And what that means is that the point (1, 16/7) is one of the 
points on the line which has 1 as its x coordinate and 16/7 as 
its y-coordinate:






Edwin