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\noindent\textbf{First solution example}:\\[1ex]
The solution for the system equation
\[ \renewcommand{\arraystretch}{1.2}
   F(x,y) = 0\quad\mbox{and}\quad
   \left|\begin{array}{ccc}
     F''_{xx} & F''_{xy} & F'_x\\
     F''_{yx} & F''_{yy} & F'_y\\
     F'_x     & F'_y     & 0
   \end{array}\right| = 0     
\]
yields the coordinates for the possible inflection points of $F(x,y) = 0$.

\bigskip
\noindent\textbf{Second solution example}:\\[1ex]
The solution for the system equation
\[ \renewcommand{\arraystretch}{1.2}
   F(x,y) = 0\quad\mbox{and}\quad\begin{array}{|ccc|}
   F''_{xx} & F''_{xy} & F'_x\\
   F''_{yx} & F''_{yy} & F'_y\\
   F'_x     & F'_y     & 0
  \end{array} = 0     
\]
yields the coordinates for the possible inflection points of $F(x,y) = 0$.
\end{document}

