The second equation can be written as $2\sqrt{2x} + 3\sqrt{y} = 35$. Together with the first equation, we obtain a system of two linear equations in the two unknowns $\sqrt{2x}$ and $\sqrt{y}$, which can easily be solved to give $\sqrt{2x} = 4$ and $\sqrt{y} = 9$. From this follows $x = 8$ and $y = 81$, so that $20x + 23y = 20 \cdot 8 + 23 \cdot 81 = 2023$.