System of Linear Differential Equations 1

$\dot { x } = 0.1 x+ 0.2y \\ \dot { y } = 0.3x+0.2y$ Given the solution to the system of ODEs above is in the form $\left[ \begin{matrix} x \\ y \end{matrix} \right] =A\left[ \begin{matrix} a \\ -b \end{matrix} \right] { e }^{ -0.1t }+B\left[ \begin{matrix} c \\ d \end{matrix} \right] { e }^{ 0.4t }$ where $a,b,c,d$ are all positive integers such that $a,b$ are coprime, and $c, d$ are coprime.

Calculate $-ad-bc$ .