Braces in equations

Question

This resembles what I want:

Unfortunately, both braces are too big. I would like the brace on the top to enclose the variables, that is, span from (x_0 to \x_i). The brace on the right should enclose only the equations. How can I fix this?

---

Code:

\begin{equation}
  \left.
  \overbrace{
  \begin{array}{l@{\,}l}
    F_1(x_0, x_1) & =0 \\
    \vdots \qquad\qquad \ddots & \\
    F_i(x_0, x_1, \dots ,x_i) & =0 \\
  \end{array}
  }^\textrm{$d_0+\cdots+d_i$\mbox{~variables}}
  \right\} \quad d_1 + \cdots + d_i \mbox{~equations}
\end{equation}

Answer 1

\documentclass{article}

\begin{document}

\begin{equation}
  \left.
  \raisebox{10pt}[30pt]{\smash{$\begin{array}{r@{}l@{\,}l}
   &  d_0+\cdots+d_i\rlap{~variables}&\\
   &  $\downbracefill$&\\
    F_1(&x_0, x_1) & =0 \\
   & \vdots \qquad\qquad \ddots & \\
    F_i(&x_0, x_1, \dots ,x_i) & =0 \\
  \end{array}$}}
  \right\} \quad d_1 + \cdots + d_i \mbox{~equations}
\end{equation}

\end{document}

I just chose the values by eye for the default font setup. By playing with the 10pt and 30pt in my answer you can make the vertical brace any size at all, and affect its vertical position. This will overprint preceding text unless you add a suitable \vspace{...} space wither before the whole equation, or if you need to embed this as a subterm, you could wrap it in a one-column array and again place some vertical space above the expression within the array.