I just learned about this technique here, but everything I find online only mentions linear equations specifically. What about systems of polynomial equations? If it doesn't work, why not?
More info: I have solved a system of polynomial equations using the elimination method and it seems to be giving me incorrect results, so I'm wondering if this is the cause. It seems to have reduced the degree of the resulting polynomial equation from 4 to 2, which seems fishy. $$ |v_n|^2 = \mathbf{v_{xn}}^2 + \mathbf{v_{yn}}^2 \tag 1 $$ $$ |v_e|^2 = \mathbf{v_{xe}}^2 + \mathbf{v_{ye}}^2 \tag 2 $$ $$ p_x = m_e \mathbf{v_{xe}} + m_n \mathbf{v_{xn}} \tag 3 $$ $$ p_y = m_e \mathbf{v_{ye}} + m_n \mathbf{v_{yn}} \tag 4 $$ Unknowns are bolded. I solved it mainly by using substitution, but at one point I used (2) to eliminate a pair of squared terms, leaving me with a linear equation on one side and a square root on the other, which, after squaring both sides, turned into a quadratic equation. I was then able to solve it using the quadratic formula, but the roots seems wrong when I substitute them back in.
(This is a followup to another question I had, if you're curious where the equations came from).
seems to be giving me incorrect results
cannot be answered unless you post your calculations. $\endgroup$