Systems of Differential Equations · Hard problem

Let $A=\begin{pmatrix}5&-2\\-2&2\end{pmatrix}$ and $\mathbf x'=A\mathbf x$ with $\mathbf x(0)=(1,1)$. As $t\to\infty$, the ratio $y(t)/x(t)$ approaches a constant slope $m$. Find $m$.