We have $A_i , B_i , C_i , D_i , E_i ,F_i, \ (i=1, 2) $.

We want to find $ (u,v) \in \mathbb{R}^2$ satisfying

\begin{equation} A_1 u^2 + B_1 uv + C_1 v^2 + D_1 u + E_1 v +F_1 =0 \\ A_2 u^2 + B_2 uv + C_2 v^2 + D_2 u + E_2 v +F_2 =0. \end{equation}

Is there a general method to find exact solution (not an approximate solution)?