X1 and X2 are zero-mean and uncorrelated. Do the coefficients from regressing y on both together match those from regressing y on one and then the residual on the other?

X1 and X2 are zero-mean and uncorrelated. You can estimate their coefficients for y in two ways. Method one: regress y on X1 and X2 together. Method two: regress y on X1, take the residual and regress it on X2 to get the X2 coefficient; then regress y on X2, take the residual and regress it on X1 to get the X1 coefficient. How do the coefficients from the two methods compare?