If x^2-y^2 = 55 and x-y=11, then what is y?

x-y = 11 => x=
11+y

Replace x=11+y in x^2 - y^2 =
55

And then, apply a^2 - b^2 =
(a-b)(a+b)

We receive

(11+y)^2
- y^2 = 55 <=> (11+y-y)(11+y+y) =
55

                                <=>
  11(11+2y)            = 55

                               
<=>   11+2y                   =
5

                               
<=>   2y                         =
-6

                                <=>    
y                         = -3.

Hope easier to
understand.