G10.1 If $b+c=3$
(1), $c+a=6$
(2), $a+b=7$
(3) and $P=a b c$, find $P$.
$\begin{array}{l}(1)+(2)-(3): 2 c=2 \Rightarrow c=1 \\ (1)+(3)-(2): 2 b=4 \Rightarrow b=2 \\ (2)+(3)-(1): 2 a=10 \Rightarrow a=5 \\ P=1 \times 2 \times 5=10\end{array}$