Using a centered model for 2 regression lines with a common slope,

Yi = { Bo(1) + B1(X_i - Xbar1) + u_i, i=1,2,...,n1
{ Bo(2) + B1(X_i - Xbar2) + u_i, i=n1+1,...n1+n2

I have to derive the least squares estimates for the three parameters (b0(1), b0(2), and b1)

I know for deriving the least squares estimates for a single model, you sum u_i squared, and take the partial derivatives of B0 and B1, set them to zero, and solve...

In this case, would I take the partial derivatives with respect to B0(1) (from the first part of the model) and equate it to the partial derivative of B0(2) (from the second part of the model)...thus giving me an answer for b0(1) in terms of b0(2) and vice versa?

Or is that totally off base...