\documentclass{article} \begin{document} \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}