Find $\alpha$ and $\beta$ that solve the following equation: \begin{equation*} \alpha\begin{bmatrix} 1 & 2 \\ 4 & 1 \end{bmatrix} + \beta\begin{bmatrix} 2 & 1 \\ 3 & 1 \end{bmatrix} = \begin{bmatrix} -1 & 4 \\ 6 & 1 \end{bmatrix} \end{equation*}