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**Keep** Here is the question:

Find the extrema of $\displaystyle f(x, y) = x + y^2$, with constraint : $\displaystyle 2x^2 + y^2 = 1$

My attempts at solution:

I tried to solve it using Lagrange multiplier and I got:

$\displaystyle 1 = 4x lambda $ ............................. I

$\displaystyle 2y = 2y lambda$ ............................. II

$\displaystyle 2x^2 + y^2 = 1 $ ............................. III

Now here is where I am stuck. How can I use the first two equations to get the value of either x or y?