Question

Solve for $x$ and $y$:$mx-ny=m^2+n^2$ and $x+y=2m$.

Answer 1

$mx-ny=m^2+n^2$

$mx+my=2m^2$

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$\overline{-my-ny=m^2+n^2-2m^2}\Rightarrow (x+y=2m)\times m$

$-y=\frac{(n^2-m^2)}{m+n}\Rightarrow y=\left(\frac{m^2-n^2}{m+n}\right)=\frac{(m+n)(m-n)}{(m+n)}$

$y=m-n$

Substitute 'y' in equaltion $x+y=2m$

$x=2m-m+n$

$x=m+n$

$(x,y)=[m+n,m-n]$