s = DSolve[{a'[t] == -k1 a[t] + km1 b[t], b'[t] == k1 a[t] - km1 b[t],  a[0] == 1, b[0] == 0}, {a[t], b[t]}, t]

s[[1,2,2]]

s[[1,1,2]]

a[t_, k1_, km1_ ] := Evaluate[s[[1,1,2]]]

b[t_, k1_, km1_ ] := Evaluate[s[[1,2,2]]]

Plot[{a[t, 0.3, 0.1], b[t, 0.3, 0.1]}, {t, 0, 100}]

Animate[Plot[{a[t, k1, km1], b[t, k1, km1]}, {t, 0, 100}, PlotRange -> {{0, 100},{0,1}}],{k1, 0.01, 1},{km1, 0.01, 1},AnimationRunning->False]