eq. 1     x+xy+1=16 
eq. 2        x-y=1,

Solve eq. 2 for x:

eq. 2        x-y=1
eq. 3          x=1+y

Substitute 1+y for x in eq. 1:

eq. 1     x+xy+1=16
  (1+y)+(1+y)y+1=16
      1+y+y+y²+1=16
         y²+2y+2=16
        y²+2y-14=0










Two solutions for y:

 and 

Use eq. 3 with first solution for y          

     x=1+y                                
     x=1+               
     x=                       

First solution:
then x+y=+()
then x+y=


Use eq. 3 with second solution for y          

     x=1+y                                
     x=1+               
     x=                       

Second solution:
then x+y=+()
then x+y=

Edwin