Jacobian Determinants (Implicit differentiation)

The equations,

$\displaystyle x^{2} + y +3s^{2} + s = 2t-1, y^{2} - x^{4} +2st +7 = 6s^{2}t^{2}$

define s and t as functions of x and y. Find $\displaystyle \frac{\partial s}{\partial x}$ when s = 0 and t = 1. Assume x > 0.

I've gone through the whole process defining the functions F and G and using Jacobian determinants to solve for $\displaystyle \frac{\partial s}{\partial x}$ but I'm still stuck with some x's in my answer that I can't figure out eliminate.

The answer listed is -16, but I after all my computation I came up with 2x^3.

You can see that if you define the first equation as a function F(s,t,x,y) = 0, and G(s,t,x,y) = 0 the partial with respect to x of equation G (-4x^3) won't go away, even after evaluating s and t at 0 and 1 repsectively.

Any ideas/suggestions?