ILL 1985 Problem 19

Solve the system of simultaneous equations $$\sqrt x - \frac 1y - 2w + 3z = 1,$$$$x + \frac{1}{y^2} - 4w^2 - 9z^2 = 3,$$$$x \sqrt x - \frac{1}{y^3} - 8w^3 + 27z^3 = -5,$$$$x^2 + \frac{1}{y^4} - 16w^4 - 81z^4 = 15.$$