Reb “anon for this”,
I never looked at it that way, but I guess it would be easier to program a computer to calculate the unknown variables as the ratio of two determinants than to pivot the equations using the Gaussian elimination method.
At first I also assumed that Cramer was the Vilna Goan. When I asked someone in yeshiva if “Cramer was the Vilna Goan”? He looked at me like I was on Coke and said “From Seinfeld”? (From then on I remembered that Gabriel Cramer spells his name with a C.)