x^2 - y^2 = 55 and x-y=11, find the value of y?

{x2−y2=55x−y=11 How can I find the value of y?

Solution:

Note that x2−y2=(x−y)(x+y)$x^2-y^2=(x-y)(x+y)$. Hence,

                                                  {x2−y2x−y=55=11

can be rewritten in the form

                                                  {x+yx−y=5=11

Adding the two equations, we obtain 2x=16$2x=16$, and we conclude that x=8$x=8$. Subtracting the two equations, we obtain 2y=−6$2y=-6$, and we conclude that y=−3$y=-3$.