Solve

mx-ny=m^{2} + n^{2 }; x+y = 2m

mx - ny = m^{2} + n^{2}

==> mx - ny = m^{2} + n^{2} +2mn - 2mn

==> mx - ny = (m + n)^{2} - 2mn [identity a^{2} + 2ab +b^{2} = (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!*

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