# Solving system of equations with hyperbolic functions

Do you maybe know how to solve a system of equations with hyperbolic functions? Imagine the problem of the form: $$x=\textrm{sech}(x^2+y^2) \\ y=1-\textrm{sech}^2 (x+y)$$ Any ideas how to solve it for x and y?

-
$sech(z)=2/(e^z+e^{-z})$ –  dato datuashvili Apr 4 '13 at 12:32
The second equation is ambiguous. Is it $\text{sech}[(x+y)^2]$ or $\text{sech}^2(x+y)$? –  Ron Gordon Apr 4 '13 at 12:33
Why the hypergeometric-function tag? Do you have a reason for thinking hypergeometric functions are relevant here? –  Gerry Myerson Apr 4 '13 at 12:34
Thanks for the remarks, my typos. –  wlq Apr 4 '13 at 12:47
use definiton of sech function ,which i have put as comment –  dato datuashvili Apr 4 '13 at 12:48