KöMaL 2010 B4317

Solve the following simultaneous equations: $\frac{1}{\sqrt{1-x^2}} + \frac{1}{\sqrt{1-y^2}} =\frac{35}{12}$, $\frac{x}{\sqrt{1-x^2}} - \frac{y}{\sqrt{1-y^2}} =\frac{7}{12}$.