Question

Solve the following for x and y
m(x+y) +n(x-y)-(m^2+mn+n^2)=0
n(x+y)+m(x-y)-(m^2-mn+n^2)=0

Answer 1

The solution for these pair of equations is

$( \frac{mn}{m - n} \: \: , \: \: \frac{ {m}^{2} + {n}^{2} }{m + n} )$