vv 12330, thank you so much.  I'm ashamed that it's taken me five years to say that but I think this is the first time since then that i've been back.  my need at that time was cancelled by my management's request to stop working on it.  Anyway I'm back now with a similar problem and I think your answer may point the way.  -tom

@tomleslie rhs works beautifully.  I had tried op(2,solution) but that didn't work in conjunction with plot.  I'll try to upload the actual sheet next time I need help so thanks for that tip too.