In this lesson, 7.3 Multivariable Linear Systems, we review how to solve systems of three linear equations using Gaussian elimination. We focus on eliminating the same variable twice, rewriting systems in row echelon form, back-substitution, and identifying when a system has one solution, no solution, or infinitely many solutions.
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Chapters:
00:00 Introduction to multi-variable linear systems
00:08 Row echelon form
00:35 Solving from row echelon form
01:26 Gaussian elimination overview
02:14 Main elimination strategy
02:35 Example: solving a 3-variable system
06:09 Back substitution
07:33 Inconsistent systems / no solution
09:48 Infinitely many solutions
11:36 Graphical interpretation of 3-variable systems
