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I have some troubles with the next exercise. I'm preparing for an exam and I have been trying to solve this with no success.

Justify that the system of equations $$ uv - 3x + 2y = 0$$ $$u^4 - v^4 = x^2 - y^2$$ defines implicitly to $u$ and $v$ as functions of $(x,y)$ in $(1,1,1,1)$ and find the equations of tangent planes to the graphs of functions $u(x,y)$ and $v(x,y)$ in $(1,1)$.

I have solved this type of exercises with an only equation but I feel a bit lost with more ones. Any advice/help to solve this?

makux_gcf
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  • This is a system $f:\mathbb{R}^2 \times \mathbb{R}^2 \to \mathbb{R}^2 $ of the form $((x,y),(u,v)) \mapsto f((x,y),(u,v))$. Compute the derivative with respect to the first parameter ($(x,y)$) and show that it is invertible. Use the implicit function theorem. – copper.hat May 06 '19 at 23:31
  • Do you still need help with this? Here's a similar example. – Git Gud May 11 '19 at 10:20

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