Chapter 17.4, Problem 20E

To determine

To show: The three equations $F_x\left(x,y,\lambda \right)=0$, $F_y\left(x,y,\lambda \right)=0$ and $F_{\lambda }\left(x,y,\lambda \right)=0$ are equivalent to $f_x\left(x,y\right)=\lambda g_x\left(x,y\right),f_y\left(x,y\right)=\lambda g_y\left(x,y\right)\text{ and g}\left(x,y\right)=0$.