2. Given $\left\{\begin{array}{l}4^{x}+y=4030, \\ 17 \times 2^{x}+2 y=2019 .\end{array}\right.$ Find all real roots of the system of equations.
2. Eliminating $y$ from the system of equations, we get
$$
2 \times 4^{x}-17 \times 2^{x}=6041 \text {. }
$$

Let $t=2^{x}$, then equation (1) becomes
$$
\begin{array}{l}
2 t^{2}-17 t-6041=0 \\
\Rightarrow t=\frac{17+\sqrt{48617}}{4} \text { (negative value discarded). }
\end{array}
$$

Thus, $x=\log _{2} \frac{17+\sqrt{48617}}{4}$,
$$
y=\frac{7787-17 \sqrt{48617}}{8} .
$$