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On number 9 from the review sheet the question asks to find the extremes of f(x, y) = 2x + 4y subject to $x^2+y^2=20$. When I was setting up my system of equations I got $$2=2\lambda x$$ $$4=2\lambda y$$ $$x^2+y^2=20$$ Then when I set them to 0 I got $$2-2\lambda x=0$$ $$4-2\lambda y=0$$ and when you simplify you are not able to pull out a variable $$2(1-\lambda x)=0$$ $$2(2-\lambda y)=0$$ My question is what do you do if this happens because the examples in my notes just have it where you are able to pull out a variable?

On number 9 from the review sheet the question asks to find the extremes of f(x, $f(x, y) = 2x + 4y 4y$ subject to $x^2+y^2=20$. When I was setting up my system of equations I got $$2=2\lambda x$$ $$4=2\lambda y$$ $$x^2+y^2=20$$ Then when I set them to 0 I got $$2-2\lambda x=0$$ $$4-2\lambda y=0$$ and when you simplify you are not able to pull out a variable $$2(1-\lambda x)=0$$ $$2(2-\lambda y)=0$$ My question is what do you do if this happens because the examples in my notes just have it where you are able to pull out a variable?

On number 9 from the review sheet the question asks to find the extremes of $f(x, y) = 2x + 4y$ subject to $x^2+y^2=20$. When I was setting up my system of equations I got $$2=2\lambda x$$ $$4=2\lambda y$$ $$x^2+y^2=20$$ Then when I set them to 0 I got $$2-2\lambda x=0$$ $$4-2\lambda y=0$$ and when you simplify you are not able to pull out a variable $$2(1-\lambda x)=0$$ $$2(2-\lambda y)=0$$ My question is what do you do if this happens because the examples in my notes just have it where you are able to pull out a variable?

On number 9 from the review sheet the question asks to find the extremes of $f(x, y) = 2x + 4y$ subject to $x^2+y^2=20$. When I was setting up my system of equations I got $$2=2\lambda x$$ $$4=2\lambda y$$ $$x^2+y^2=20$$ Then when I set them to 0 I got $$2-2\lambda x=0$$ $$4-2\lambda y=0$$ and when you simplify you are not able to pull out a variable $$2(1-\lambda x)=0$$ $$2(2-\lambda y)=0$$ My question is what do you do if this happens because the examples in my notes just have it where you are able to pull out a variable?