Procedural flexibility refers to the ability to choose efficient strategies for the solution of problems. We study procedural flexibility and accuracy when solving linear and quadratic equations as well as in systems of equations at the beginning of university mathematics. We also investigate the viability of the chosen domains for measuring flexibility in the setting of a tri-phase test. We conclude that university students show procedural flexibility and that accuracy and flexibility correlate positively with their course success. This contrasts the earlier results that only accuracy had a significant positive correlation with results of a delayed test among high school students. Finally, we show that we can measure flexibility for both quadratic equations and systems of equations.