8. Solve the system $\left\{\begin{array}{l}3^{y} \cdot 81=9^{x^{2}} ; \\ \lg y=\lg x-\lg 0.5 .\end{array}\right.$
Solution: $\left\{\begin{array}{l}3^{y} \cdot 81=9^{x^{2}}, \\ \lg y=\lg 2 x,\end{array} 3^{2 x} \cdot 9^{2}=9^{x^{2}}, x+2=x^{2}, x^{2}-x-2=0\right.$, $\left\{\begin{array}{l}x=-1-\text { n.s., } \\ x=2,\end{array} \Rightarrow x=2 \Rightarrow y=4\right.$. Verification: $\left\{\begin{array}{l}3^{4} \cdot 81=9^{4}, \\ \lg 4=\lg (2 \cdot 2) .\end{array}\right.$

Answer: $x=2$.