Clear[x,y,t]
eqs={x'[t]+y[t]==1,y'[t]+2x[t]==0}
cnd={x[0]==0,y[0]==0}
fns={x[t],y[t]}
DSolve[Union[eqs,cnd],fns,t]/.t->1//N
InverseLaplaceTransform[Solve[LaplaceTransform[eqs,t,s],LaplaceTransform[fns,t,s]],s,t]/.Map[Apply[Rule,#]&,cnd]
{x[t],y[t]}/.%/.t->1//N