many thanks for this i have implemented all of your comments except the first i ahve altered the explanation about 'values of solutions' to make it i hope clearer just what i mean i have managed to alter the diagrams as you suggest using inkscape which i downloaded a few days ago i would welcome your help pages about this as my first attempts at creating diagrams were unsuccessful all the lines text etc whihc i created came out in light grey rather than black even though i set it at black using the fill so either i am doing something very stupid or there is some setting which i am missing i am now going to make the page live thanks again