Max-Sharpe weight in A with a fully invested budget

Assets $A$ and $B$ have expected excess returns of $7\%$ and $4\%$, and their excess returns have covariance matrix $\begin{bmatrix}1&1\\1&2\end{bmatrix}$. You hold $a$ units of $A$ and $b$ units of $B$ with $a+b=1$ (short positions allowed). What value of $a$ maximises the portfolio's Sharpe ratio?

$a=10/7$. The maximum-Sharpe (tangency) weights are proportional to $\Sigma^{-1}\mu=\begin{bmatrix}2&-1\\-1&1\end{bmatrix}\begin{bmatrix}7\\4\end{bmatrix}=\begin{bmatrix}10\\-3\end{bmatrix}$. Scaling to sum to one gives $a=\tfrac{10}{7}$ and $b=-\tfrac37$.