SUMMARY
Algebra is a branch of mathematics that uses mathematical statements to describe the relationship between various things. This study aims to describe the algebra problem solving abilities of students in the Linear Program course. There are differences in student problem solving, which are caused by students' cognitive styles. Reflective and impulsive cognitive styles based on the SOLO taxonomy. This research method is descriptive qualitative. The research was conducted at STKIP Kusuma Negara Jakarta. The research subjects consisted of 4 students, 2 students having a reflective cognitive style and 2 students having an impulsive style. Purposive sampling technique was used in taking the subjects.Data collection techniques used cognitive style test questions Matching Familiar Figures Test (MFFT), algebra problem solving test questions and interview guidelines. Data collection techniques used two techniques, namely written tests and interviews. Technical analysis of data by reducing data, presenting data, and drawing conclusions. From the data processing, the results of the research were 2 students whose have flexible cognitive style also have good algebra problem solving abilities and based on SOLO taxonomy reached the Extended abstract level. Meanwhile, students who have an impulsive cognitive style in solving algebra problems based more on the SOLO taxonomy have Multistructural and Unistructural levels. So each cognitive style of students gives the different results in solving problems.