# Is it possible to solve this system of equations? [duplicate]

This question already has an answer here:

Consider a system of equations given below:

$p_1 + p_2 + p_3 + p_4 + p_5 = 1$

$x_1*p_1 + x_2*p_2 + x_3*p_3 +x_4*p_4 =0$

$x_1^2*p_1 + x_2^2*p_2 + x_3^2*p_3 +x_4^2*p_4 =1$

$x_1^3*p_1 + x_2^3*p_2 + x_3^3*p_3 +x_4^3*p_4 =v_1$

$x_1^4*p_1 + x_2^4*p_2 + x_3^4*p_3 +x_4^4*p_4 =v_2$

$x_1^5*p_1 + x_2^5*p_2 + x_3^5*p_3 +x_4^5*p_4 =v_3$

$x_1^6*p_1 + x_2^6*p_2 + x_3^6*p_3 +x_4^6*p_4 =v_4$

$x_1^7*p_1 + x_2^7*p_2 + x_3^7*p_3 +x_4^7*p_4 =v_5$

$x_1^8*p_1 + x_2^8*p_2 + x_3^8*p_3 +x_4^8*p_4 =v_6$

Is there a method to solve $x_i$ and $p_i$ in terms of $v_i$?

Thank You!