<s>[INST] Consider the dynamical system governed by the system of equations: 
$$\begin{cases}
\frac{dx}{dt} = 2x - 4y + t^2\\
\frac{dy}{dt} = x - 2y + 3t
\end{cases}$$ 
where $x(0) = 1$ and $y(0) = 2$. Convert this into a system of first-order linear differential equations for the variables $x, y$, and $t$.[/INST]