I'm looking for a general method to find at least one solution to the system below
$$a_0 = a_1x_1 + \cdots + a_nx_n$$
$$b_0 = b_1x_1 + \cdots + b_nx_n$$
$$c_0 = c_1x_1 + \cdots + c_nx_n$$
$$d_0 = d_1x_1 + \cdots + d_nx_n$$
$$x_1 + \cdots + x_n = 1$$ $$0\le x_1, \dots , x_n \le 1$$
where $a_i, b_i, c_i, d_i$ are known real numbers, $x_i$ are unknown and $n > 20$.
Thank you in advance.