jmc

Summing all three equations yields that $5a+5b+5c=-3+9+19=25$. Thus, $a+b+c=5$. Subtracting this from each of the given equations, we obtain that $2a=-8,2b=4,2c=14$. Thus, $a=-4,b=2,c=7$, and their product is $abc=-4\times 2\times 7=\boxed{-56}$.