Combined Nonlinear Systems of Equations and Inequalities

$\begin{cases}5^x+5^y<10\\5^{-x}+5^{-y}<10\\x^2+y^2=36\end{cases}$

$\begin{cases}2^x+2^y<100\\2^{-x}+2^{-y}<100\\x^2+y^2=49\end{cases}$

$\begin{cases}10^x+10^y<50\\10^{-x}+10^{-y}<50\\x^2+y^2=64\end{cases}$