Question 101
Real numbers $x_1,\ldots,x_{30}$ satisfy
$$\begin{cases}20^3x_1+21^3x_2+\cdots+49^3x_{30}=13,\\21^3x_1+22^3x_2+\cdots+50^3x_{30}=1,\\22^3x_1+23^3x_2+\cdots+51^3x_{30}=19.\end{cases}$$
Find $21x_1+22x_2+\cdots+50x_{30}$.
(A) More than one value is possible
(B) The system has no solution
(C)1065
(D)7
(E)5
$$\begin{cases}20^3x_1+21^3x_2+\cdots+49^3x_{30}=13,\\21^3x_1+22^3x_2+\cdots+50^3x_{30}=1,\\22^3x_1+23^3x_2+\cdots+51^3x_{30}=19.\end{cases}$$
Find $21x_1+22x_2+\cdots+50x_{30}$.
(A) More than one value is possible
(B) The system has no solution
(C)1065
(D)7
(E)5