How can I solve two related non-linear equations using EDP finite volume method?

[zaynab]

Hi evryone,
the system i am working on, is composed of two relatied non-linear equations that I discretised using finite volume method with fully implicit scheme, the difficulty is that the two unknonw appear in both equations and i don't know how to solve it.

Any propositions?
Thank you.

 

[zaynab]

Sorry, i corrected the system: