Solve
mx-ny=m2 + n2 ; x+y = 2m
mx - ny = m2 + n2
==> mx - ny = m2 + n2 +2mn - 2mn
==> mx - ny = (m + n)2 - 2mn [identity a2 + 2ab +b2 = (a+b)2] ---> 1
x + y = 2m ---> 2
Substituting eq. 2 in eq. 1.
mx - ny = (m + n)2 - (x + y)n
mx - ny = (m + n)2 - nx - ny
Addding ny to both sides, you get:
mx = (m + n)2 - nx
mx + nx = (m + n)2
x(m + n) = (m + n)2
Dividing both sides by (m + n), you get:
x = m + n
Substituting x = m + 2 in eq. 1.:
(m + n) + y = 2m
y = 2m - m - n
y = m - n
Therefore, x = m + 2, y = m - n
Hope that helped... Thank you!