In one physics problem, I got the following system of non-linear equations that I need to solve for $v_e$, $v_s$ and $\omega$:
$m_p v_a = m_s v_s + m_p v_e$
$\frac{l}{2} m_p v_a = \frac{l}{2} m_p v_e + I \omega$
$\frac{1}{2} m_p v_a^2 = \frac{1}{2} m_p v_e^2 + \frac{1}{2} m_s v_s^2 + \frac{1}{2} I \omega^2$
I know how to solve this with substitution and a lot of scratch paper.
With linear systems, one can just derive the matrix and use gauss-jordan / reduced row echolon form and then the solution is directly apparent.
Is there something handy for non-linear equations as well?