I have N equations and am having trouble with finding a solution.
$\left\{\begin{matrix} x_1 y_1 = \sum_{i=1}^N x_i\\ x_2 y_2 = \sum_{i=1}^N x_i\\ \vdots\\ x_N y_N = \sum_{i=1}^N x_i \end{matrix}\right.$
where $x_i$, ($i = 1, 2, \cdots, N$) is an unknown and $y_i$, ($i = 1, 2, \cdots, N$) is a known variable.
Given $y_i$'s, I have to find $x_i$'s but, I don't know where to start and even if it has a solution.