I have four polynomials with four unknowns $x_{1},x_{2},y_{1}$ and $y_{2}$ as following $$ \left\{ \begin{array}{c} m_{1} + m_{2}x_{1} + (m_{5} + m_{6}x_{2})y_{1} + (m_{3}+m_{4}x_{1})y_{2} ==0 \\ n_{1} + n_{2}x_{1} + (n_{3} + n_{4}x_{1})y_{1} + n_{5}x_{2}y_{2} ==0 \\ x_{1}^{2} + x_{2}^{2} = 1\\ y_{1}^{2} + y_{2}^{2} = 1\\ \end{array}, \right. $$ where $m_{1}$, $m_{2}$, $m_{3}$, $m_{4}$, $m_{5}$, $m_{6}$, $n_{1}$, $n_{2}$, $n_{3}$, $n_{4}$ and $n_{5}$ are unknown real values. Does anyone know there is someway to eliminate any of the three variables, and then get an equation with only one variable. I use Mathematica, it compute a long time... and I havent got it yet.
Thank you.