# Solving systems of equations from dynamics

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 $M$, $m$, $\mu_S$, $\theta$.

$$N\sin\theta−\mu_SN\cos\theta=ma$$ $$N\cos\theta+\mu_SN\sin\theta−mg=0$$ $$−N\sin\theta+\mu_SN\cos\theta+F = Ma$$

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I replaced the example. –  dal102 Feb 24 '13 at 5:13

What you have been told, is false. The system $x+y=1,x+y=17$ has as many equations as unknowns, yet it has no solution.