s=NDSolve[{x'[t] == x[t]*(1 - x[t]) - 9*x[t]*y[t]/(10*x[t] + 1),
            y'[t] == 0.3*y[t]*(1 - 10*y[t]/(10*x[t] + 1)), x[0] == 0.15, y[0] == 0.25},
            {x, y}, {t, 0, 150}]

 Plot[Evaluate[x[t] /. s], {t, 0, 150}, PlotRange -> All]
 Plot[Evaluate[y[t] /. s], {t, 0, 150}, PlotRange -> All]