Determine if bounded solutions of ODE system are stable Please help me to handle the following problem:

Prove or disprove that bounded solutions of ODE system $$\dot x = 3x + y + 1; \dot y = 6x+2y+2$$ are stable using a theorem about stability of linear systems.

My progress:

What I was able to prove is that bounded solutions of this system have the form $x =c, y= -1-3c$, where $c \in \mathbb{R}$. I can post my solution about it upon request. But I do not see how to apply a theorem about the stability of linear systems here. For me it is clear that bounded solutions are stable: any bounded solution is fully determined by initial conditions and constant so you can just use the definition of stability. But I have to use a theorem about stability of linear system, and I do not see how to do it.

Thanks a lot for your hints and answers!
Step 1: Apply the Laplace transform to both equations and solve the system in the Laplace domain. The system becomes linear in the Laplace domain and it is, therefore, easy to solve.

Step 2: If the solution's poles are in the second or third quadrant the system is stable and therefore your solutions to the system are too.

I would apply the Routh–Hurwitz stability criterion- 

https://en.wikipedia.org/wiki/Routh%E2%80%93Hurwitz_stability_criterion
http://pages.mtu.edu/~tbco/cm416/routh.html

The method above is normally used by Control Engineers to check the stability of LTI systems.
Step 1: Apply the Laplace transform to both equations and solve the system in the Laplace domain. The system becomes linear in the Laplace domain and it is, therefore, easy to solve.

Step 2: If the solution's poles are in the second or third quadrant the system is stable and therefore your solutions to the system are too.

I would apply the Routh–Hurwitz stability criterion- 

https://en.wikipedia.org/wiki/Routh%E2%80%93Hurwitz_stability_criterion
http://pages.mtu.edu/~tbco/cm416/routh.html

The method above is normally used by Control Engineers to check the stability of LTI systems.