Cramer's Rule vs GEPP for 2 by 2 - any recent opinions/analysis

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I need to solve a simple set of 2 by 2 equations for a project.
The project specifies a formula in the specification (cramer's rule it seems) and I see some indication in various places on the web (including a paper by Cleve Moler fom 1974( that Gaussian Elimination with Partial Pivoting is a better choice for stability.
Is there any other analysis? Should I check the condition number of my input data or write both and compare the results? (I'm writing this in C++ code with double precision fp). Thanks
Rick

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