Partial derivative using differentials

1. The problem statement, all variables and given/known data

If [itex] xs^2 + yt^2 = 1 [/itex] and [itex] x^2s + y^2t = xy - 4 [/itex], find [itex] \frac{\partial x}{\partial s}, \frac{\partial x}{\partial t}, \frac{\partial y}{\partial s}, \frac{\partial y}{\partial t} [/itex], at (x, y, s, t) = (1, -3, 2, -1)





2. Relevant equations









3. The attempt at a solution

I took the differential of both equations and substituted in the values and I got:



[tex] 4ds + 4dx + 6dt + dy = 0 [/tex] and

[tex] ds + 7dx + 9dt + 5dy = 0 [/tex]



but now I don't know how do find the individual partial derivatives that are being asked for. For example, for [itex] \frac{\partial x}{\partial s} [/itex], I assumed t and y are constant and made dt and dy = 0 and tried to solve for ds and dx but that doesn't work.



Any ideas on how to proceed in finding these partials?

Thanks!