Answer:

One choice is: s = S/ K, $x = X/(K \, y_{XS})$, $\tau = t \, j_S \, y_{XS}$. The system then becomes

$$\begin{eqnarray*}\frac{d} {d\tau} s & = & - f x\\ \frac{d} {d\tau} x & = & f x \end{eqnarray*}$$

with $f = \frac{s} {1 + s}$ and two parameters: s(0) = S(0)/ K, $x(0) = X(0)/(K \, y_{XS})$.