Take the 2-minute tour ×  I am trying to show that the following
equation system:  $$e^u+e^v+2-4e^{x^2-y}=0$$ $$\sin
u+xu-v^4-y=0$$  Does not define $(y,x)$ as a function of $(u,v)$
implicitly around $(0,0,0,0)$.  Attempt What I tried to do was
find $u,v$ such that in a small radius of (0,0,0,0) the equation
would have no solution. My best guess was $u=0, v=R$ (where $R
=$ radius), but I had difficulty showing that the system then
has no solution.  Help would be appreciated, and thanks in
advance!  share|improve this question Differentiate implicitely
with respect to u and v and evaluate at 0. Then see if the
Jacobian matrix is singular. –  PAD Jul 5 '12 at 7:32 We hadn't
learned this technique yet (this is a question from a former
exam I'm prepping with)... is there another solution? –  ro44
Jul 5 '12 at 7:41 @ro44 You need to use the implicit function
theorem. –  fpqc Jul 5 '12 at 7:49 @BenjaLim: I know a version
of the implicit function theorem that would let me prove this is
an implicit function, but not