@Carl Love are you implying that when Maple's solve() seems to get stuck is because the system has no solution?

I am new to Maple, I am just trying to understand if it's my system that is inconsistent or if there are alternatives to solve() that I can test on my problem at hand. Since the system is not linear in the lambdas, it's not straightforward to assess whether is inconsistent or not (what do you suggest?).

Did you check my script?

problemaple.mw

Thank you! (I am new to Maple)