It is correct ! though long !
I'll show you how I would do (and I guess it's faster...)
(x+y)(x-y)=77
11(x-y)=77
Divide by 11 :
x-y=7
And we had x+y=11.
Add these two equations term by term, because you have -y and y.
This gives (x-y)+(x+y)=7+11
2x=18
Do you see which steps look simpler ?