Hey homalina.

If this is a general linear regression, try using the fact to relate the design matrix of the new system and its parameter estimates to the design matrix of the old system with its own parameter estimates.

We know that B_hat = (X^T*X)^-1*X^TY for a particular design matrix X and a response vector Y.

If you are doing the proof for a general linear regression with the normality assumptions you will need the above. If it's for a simple linear regression of y vs x then you can use the simpler result.