B. The system of equations in $x, y, z$
$$
\left\{\begin{array}{l}
x y+y z+z x=1, \\
5 x+8 y+9 z=12
\end{array}\right.
$$

all real solutions $(x, y, z)$ are $\qquad$
$\begin{array}{l}\text { B. }\left(1, \frac{1}{2}, \frac{1}{3}\right) . \\ \quad \text { Substitute } z=\frac{1}{9}(12-5 x-8 y) \text { into } x y+y z+z x \\ =1 \text {, we get } \\ \quad 5 x^{2}+8 y^{2}+4 x y-12 x-12 y+9=0 \\ \Rightarrow(4 y+x-3)^{2}+9(x-1)^{2}=0 \\ \Rightarrow x-1=0,4 y+x-3=0 \\ \Rightarrow x=1, y=\frac{1}{2}, z=\frac{1}{3} .\end{array}$