Don't think too hard on this one

Algebra Level 4

If the two system of equations

{ax+by=13xy=2\begin{cases} ax+by=1\\ 3x-y=2\\ \end{cases}

{x+2y=1axby=2\begin{cases} x+2y=1\\ ax-by=-2\\ \end{cases}

has the same solution (x,y)(x,y), then the value of a+ba+b is mn\frac{m}{n} for relatively prime mm and nn. Find m+nm+n.

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