Solve for x and y:mx−ny=m2+n2 and x+y=2m.
mx−ny=m2+n2 mx+my=2m2
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¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯−my−ny=m2+n2−2m2⇒(x+y=2m)×m
−y=(n2−m2)m+n⇒y=(m2−n2m+n)=(m+n)(m−n)(m+n)
y=m−n
Substitute 'y' in equaltion x+y=2m
x=2m−m+n
x=m+n
(x,y)=[m+n,m−n]
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