Systems of Differential Equations · Superchallenge problem

Every solution of $x'=-x+4y,\ y'=-x-y$ satisfies an estimate $\lVert\mathbf x(t)\rVert\le C\,e^{-t}\lVert\mathbf x(0)\rVert$ for all $t\ge0$ (Euclidean length). Find the smallest constant $C$ that works for every solution.