I am studying first year undergraduate physics and am having difficulty solving the systems of equations that emerge from dynamics problems.
If I have as many equations as unknowns, I've been told the system has the possibility of being solved. How do I know if the equations are sufficient to solve? [Should each equation contain each variable?]
I'm familiar with elimination and substitution. Are there some guidelines for the cleanest approaches to systems of equations?
Here is an example of a system I might have to solve for $F$, given $M$, $m$, $\mu_S$, $\theta$.
$$N\sin\theta−\mu_SN\cos\theta=ma$$ $$ N\cos\theta+\mu_SN\sin\theta−mg=0$$ $$−N\sin\theta+\mu_SN\cos\theta+F = Ma$$