# Drawing inferences about equation solving

I have two systems of non-linear equations. The equations are continuously differentiable in the domain that I am interested in.

Let $x_1, y_1$ solve the following system of equations.

$f(x,y)=0\\ g(x,y)=0$

Let $x_2,y_2$ solve

$f(x,y)=0\\ g(x,y)=c$

Were $c>0$ is a constant. For simplicity and for starters we can assume that these solutions are unique. I have the functional forms of $f$ and $g$ and they are very long, painful and non-linear. I have some non-math intuition that the following are true and I would love some help and suggestions on the things I can try to do to prove these statements:

$x_2 > x_1 \\ y_2 > y_1 \\ x_2-x_1 > y_2-y_1$

Thanks a lot,

EDIT

Please feel free to make simplifying assumptions. For example, we can take $c>0$ to arbitrarily small for starters and see where that takes us.

I'm not sure if I can show this but suppose $f(x,y)$ and $g(x,y)$ satisfied the implicit function theorem then perhaps we could get some traction on this.

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@amWhy Thank you. I will drop the subscripts. – Amatya Nov 20 '12 at 22:56
Thanks, Amatya! I just wanted to be sure I understood the question. – amWhy Nov 20 '12 at 22:59