$\text { For } f ( x , y ) = x ^ { 2 } - x y + y ^ { 2 } - 5 x + y \text { find all values of } x \text { and } y \text { such that } f _ { x } ( x , y ) = 0$ and $f _ { y } ( x , y ) = 0$ simultaneously.
A) $x = 4 ; y = 2$
B) $x = 3 ; y = 1$
C) $x = 5 ; y = 1$
D) $x = 7 ; y = 3$
E) $x = 2 , y = 0$

Question

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The Answer of $\text { For } f ( x , y ) = x ^ { 2 } - x y + y ^ { 2 } - 5 x + y \text { find all values of } x \text { and } y \text { such that } f _ { x } ( x , y ) = 0$ and $f _ { y } ( x , y ) = 0$ simultaneously.
A) $x = 4 ; y = 2$
B) $x = 3 ; y = 1$
C) $x = 5 ; y = 1$
D) $x = 7 ; y = 3$
E) $x = 2 , y = 0$

And fy(x,y)=0f _ { y } ( x , y ) = 0fy​(x,y)=0

And $f _ { y } ( x , y ) = 0$