8. Solve the system $\left\{\begin{array}{l}\log _{4} x-\log _{2} y=0 \\ x^{2}-5 y^{2}+4=0 .\end{array}\right.$
Solution: $\left\{\begin{array}{l}\frac{1}{2} \log _{2} x-\log _{2} y=0 ; \log _{2} \frac{\sqrt{x}}{y}=\log _{2} 1, \sqrt{x}=y, \\ x^{2}-5 y^{2}+4=0, \quad x^{2}-5 x+4=0,\end{array} \Rightarrow \begin{array}{l}x=1 ; 4, \\ y=4 ; 2 .\end{array}\right.$

Answer: $\{1 ; 1\},\{4 ; 2\}$.