Determine the number of solutions to a system of equations in three variables

What you'll learn

• Identify the geometric representation (planes) of a system of three linear equations in three variables and relate it to the number of solutions (zero, one, or infinite) with 80% accuracy on a formative assessment.
• Apply algebraic techniques, including Gaussian elimination and row reduction, to transform a system of three linear equations in three variables into row-echelon form to determine if the system has no solution, a unique solution, or infinitely many solutions in at least 3 out of 4 attempted problems.
• Analyze a system of three linear equations in three variables, presented in various forms, to determine the number of solutions (none, one, or infinite) and justify the conclusion based on the resulting row-echelon form with a written explanation demonstrating understanding of the relationship between the algebraic manipulation and the geometric interpretation in a short answer question.
• Calculate the determinant of the coefficient matrix of a 3x3 system of linear equations and utilize the determinant to determine if the system has a unique solution, demonstrating accurate calculation in at least 2 out of 3 problems.