Chapter 9 - Multiveriable Calculus - 9.2 Partial Derivatives - 9.2 Exercises - Page 478: 34

$x=\frac{-13}{3}, y=\frac{14}{3}$

$f_{x}(x,y)=4 +2x + y=0$ $f_{y}(x,y)=-5 + 2y + x=0$ Solving the second equation for yields $x=5-2y$ Substituting this into the first equation yields $4+2(5-2y)+y=0$ $4+10-4y+y=0$ $y=\frac{14}{3}$ $\rightarrow x=\frac{-13}{3}$