sigh

Let the ordered triples $(x,y,z)$ of complex numbers that satisfy

$\begin{align*} x + yz &= 7, \\ y + xz &= 10, \\ z + xy &= 10. \end{align*}$

be $(x_1,y_1,z_1), (x_2,y_2,z_2), \dots, (x_n,y_n,z_n).$ Find $x_1 + x_2 + \dots + x_n.$