Home/Algebra/Polynomials/System of polynomial equations11. PolynomialsSystem of polynomial equationsLevel: avanzadoIn 11. PolynomialsFormulaCopy LaTeX{P1(x1,…,xn)=0⋮Pm(x1,…,xn)=0.\begin{cases} P_1(x_1,\ldots,x_n)=0\\ \vdots\\ P_m(x_1,\ldots,x_n)=0. \end{cases}⎩⎨⎧P1(x1,…,xn)=0⋮Pm(x1,…,xn)=0.Tagsalgebraalgebra formulapolynomialsDetailFinds points that simultaneously satisfy several polynomials.Explore the ideaFound an error? Contact us.Related formulasRelated2×2 linear system{a1x+b1y=c1a2x+b2y=c2\begin{cases}a_1x+b_1y=c_1\\a_2x+b_2y=c_2\end{cases}{a1x+b1y=c1a2x+b2y=c2Open formulaOpen in sectionRelatedMultivariable polynomialP(x1,…,xn)=∑αcαx1α1⋯xnαn,P(x_1,\ldots,x_n) = \sum_{\boldsymbol\alpha}c_{\boldsymbol\alpha} x_1^{\alpha_1}\cdots x_n^{\alpha_n},P(x1,…,xn)=α∑cαx1α1⋯xnαn,Open formulaOpen in sectionRelatedResultant and Sylvester matrixRes(f,g)=detS(f,g).\operatorname{Res}(f,g) = \det S(f,g).Res(f,g)=detS(f,g).Open formulaOpen in section