How could I solve the following system of equations:
$$xn_1^y+z=m_1$$ $$xn_2^y+z=m_2$$ $$xn_3^y+z=m_3$$ where $n_k$ and $m_k$ are parameters?
I am looking for an exact answer, but if it is not feasible, then a rough description of a numerical approach would be appreciated. Thank you.