I'm running an HP Prime on the newest firmware version, and went to solve the following system of equations in the solve app:
After inputting the values and going to the solve numeric view, pressing Solve results in a message saying "Cannot find solution". I've verified that this solution is solvable with the solution (Y=45, X=126). Can anyone explain why the Prime can't solve this, or if I'm doing something wrong?
The reason why the solving is not working for you is because it is using a "numerical" method in the solve app. Numerical methods you can think of as a very fast, "guess and check" that will converge to a number that is "close enough". If your initial guesses are too far off - especially in misbehaved or very large changing functions - they do not converge unless close. Your functions are very steep and do not behave nicely in this instance with your initial guesses.
Put some intial guesses in the solve app closer to your result, and it WILL jump to them like you expect.
Although I work for the HP calculator group as a head developer of the HP Prime, the views and opinions I post here are my own.