Big Ideas Math [IM1]: 5.4 - Solving Special Systems of Linear Equations (Lecture & Problem Set)

Special cases get their own section, which as always means although we get to practice these a great deal, don't assume that when it comes to test time we can live in this vacuum of when special cases occur. They can arise whenever at that time, so get your practice in now and know what it means as they do.

The special cases we are referring to are "infinitely many solutions" and "no solution" cases. We have seen these before. Infinitely many solutions occur when variables cancel and a true statement is made (such as 0 = 0), and no solution occurs when variables cancel and a false statement is made (such as 0 = 2). This is in a system of equations, so algebraically you will see this when attempting to solve using the substitution or elimination methods.

Graphically, infinitely many solutions occurs in a system when both equations represent the exact same line, or in slope-intercept form you will see the same slope and same y-intercept. No solutions will appear graphically as parallel lines (same slope, different y-intercepts). One solution, of course, is when two lines intersect at only one point (different slopes), which we saw a significant amount of in 5.1.

They provide a few word problems as well, and they are interesting to have a discussion on when special cases form, but real-life applications can indeed be had in these situations.

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(00:00) Introduction
(01:30) Lecture overview
(09:58) Problem #1-2
(11:37) Problem #3-8
(21:31) Problem #9-16
(31:34) Problem #17-22
(38:54) Problem #23-24
(43:46) Problem #25-26
(49:36) Problem #27
(53:58) Problem #28
(55:13) Problem #29
(55:58) Problem #30
(57:55) Problem #31
(59:24) Problem #32

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