\begin{array}{l}(x_1^4+\cdots+x_n^4)a+(x_1^3+\cdots+x_n^3)b+(x_1^2+\cdots+x_n^2)c=x_1^2y_1+\cdots+x_n^2y_n,\\ (x_1^3+\cdots+x_n^3)a+(x_1^2+\cdots+x_n^2)b+(x_1+\cdots+x_n)c=x_1y_1+\cdots+x_ny_n,\\ (x_1^2+\cdots+x_n^2)a+(x_1+\cdots+x_n)b+nc=y_1+\cdots+y_n.\end{array}