Systems of Equations · Superchallenge problem

Nine numbers $x_1, x_2, \ldots, x_9$ satisfy the nine equations $x_1 + x_2 = 1$, $x_2 + x_3 = 2$, $x_3 + x_4 = 3$, $\ldots$, $x_8 + x_9 = 8$, and $x_9 + x_1 = 9$. Find $x_1$.