Chapter 2.4, Problem 5E

In Exercises 5-12, we consider the partially decoupled system
$\begin{array}{l}\frac{dx}{dt}=2x+2y\\ \frac{dy}{dt}=-y\end{array}$

5. Although we can use the method described in this section to derive the general solution to this system, why should we immediately know that $Y\left(t\right)=\left(x\left(t\right),y\left(t\right)\right)=\left(e^{2t}-e^{-t},e^{-2t}\right)$is not a solution to the system?