So I have a question:

I need to derive an expression for the share of wealth allocated to Asset 1 in a portfolio that has the minimum possible variance. The following is known:

Two risky assets: 1 and 2
Returns: r1 and r2
Variance: σ12 and σ22
Covariance: σ12

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So thus far, I have portfolio return as:
E[rp] = w1E[r1] + w2E[r2]
=
w1E[r1] + (1 - w1)

And portfolio variance :
σp2 = w12σ12 + w22σ22 + 2w1w2σ1σ2ρ12

Substituting a formula for Corr12: ρ12 = σ12/σ1σ2 :
σp2 = w12σ12 + w22σ22 + 2w1w2σ1σ2*(σ12/σ1σ2)
=
w12σ12 + w22σ22 + 2w1w2σ12

So to minimise said portfolio, I would set up a Lagrangian Constrained Optimization as follows:
y = w12σ12 + w22σ22 + 2w1w2σ12 + λ(w1 + w2 - 1)
such that y/
w1 = 0
y/w2 = 0
y/∂λ = 0

But, from here, I am a tad lost as to how I can reconstruct this to derive a formula for w1 with minimum variance. Any help appreciated.