Conceptions about systems of linear equations of 3x2 with an empty solution: an exploratory study with university students

Abstract

The objective of the present study is to identify the conceptions that first-year undergraduate students have when faced with questions that involve solving a 3x2 systems of linear equations (SLE) with an empty solution. The data collection instrument was a diagnostic evaluation applied to 60 students enrolled in linear algebra who were starting to study SLE. The results showed that students had three different conceptions about the solution of a 3x2 SLE with an empty solution: 1) the 3x2 SLE has no solution, 2) the 3x2 SLE has three solutions because lines intersect at 3 points or there are 3 interceptions, and 3) the 3x2 SLE has one unique solution. It is concluded that these misconceptions suggest that students lack understanding of the meaning of SLE solutions and that, for this reason, students have difficulties solving SLEs that are presented graphically or analytically.