System of equations

Algebra Level pending

If the values for \(m\) for which the system of equations \(3x+my=m\) and \(2x-5y=20\) have solutions satisfying the conditions \(x>0,\quad y>0\) can be written as

\(m\in \left( -\infty ,\frac { -a }{ b } \right) \cup \left( c,\infty \right)\), where a and b are positive coprime integers.

then find the value of \(a+b+c\)

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