HMMT 2002 U44

The unknown real numbers $x, y, z$ satisfy the equations

$$\frac{x+y}{1+z}=\frac{1-z+z^{2}}{x^{2}-x y+y^{2}} ; \frac{x-y}{3-z}=\frac{9+3 z+z^{2}}{x^{2}+x y+y^{2}}$$

Find $x$.