Hello! First of all I'd like somebody to check if what I'm doing is correct. Second question: see end

I need to find the extrema of 6 - 4x - 3y subject to x² + y² = 1.

∂f/∂x = -4 and∂g/∂x = 2x and∂f/∂y = -3 and∂g/∂y = 2y

So we've got:

{ -4 = 2λx

{ -3 = 2λy

{ x² + y² = 1

<=>

{ -2/x =λ±4/5

{ -3/2y = λ

{ x² + y² = 1

If -2/x = -3/2y then 3x = 4y, this means 3x/4 = y

Substitute this into contraint:

x² + (3x/4)² = 1 <=> 25x² - 16 = 0 <=> x =

If y = 3x/4, then 3(±4/5) / 4 = ±3/5

Now here comes my second question. Now that I've gotx = ±4/5 andy = ±3/5, how do I know that the points are

(4/5, 3/5) and (-4/5, -3/5)

OR

(4/5, 3/5) , (-4/5; -3/5) , (4/5; -3/5) , (-4/5, 3/5) ?

Thanks!