# analytic solution of system of non-linear algebraic equations

Can we solve analytically a system of non-linear algebraic equations? In particular something of this form( $x_k$ are the unknowns): $$b_1 = a_{11}x_1 + a_{12}x_2+....+ a_{1k}x_k$$ $$b_2 = a_{21}x_1^2 + a_{22}x_2^2 + .....+ a_{2k}x_k^2$$ $$b_3 = a_{31}x_1^3 + a_{32}x_2^3 + ......+ a_{3k}x_k^3$$

Please suggest some material which deals with analytic solution of system of non-linear equations. thanks

• Do you mean $x=x_1$ ? Could we use Vandermonde ? – Dietrich Burde Feb 12 '16 at 15:44
• I just edited it. I know about Vandermonde matrix. How to use it here? thanks – user304876 Feb 12 '16 at 15:52