I want to show that the slope coefficient for the jth regressor for $i = 1, \dots, 2$ and $j = 1, \dots, k$ is given as
$$ b_j = \frac{Cov(y_j, u{_{ji}})}{Var(u_{ji})}$$
where $u_{ji}$ is the residual from a regression of $x_{ji}$ on all other covariates.