# Just require a substitution!

Algebra Level 4

$\begin{cases}5 x\left(1+\frac { 1 }{ { x }^{ 2 }+y^{ 2 } } \right)=12\\ 5y \left(1-\frac { 1 }{ { x }^{ 2 }+{ y }^{ 2 } } \right)=4 \end{cases}$ If $$x=a$$ and $$y=b$$ satisfy the above equations simultaneously for $$a>b>0$$, then find $$a+b$$.

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