Systems of Linear Equations
Until now, we have been working with single equations. We have seen equations with one variable, which generally have a finite number of solutions, and equations with two variables, which are usually satisfied by an infinite number of ordered pairs. In this section, we will begin to deal with systems of equations; that is, with a set of two or more equations with the same variables. We limit our discussion to systems of linear equations, since our techniques for solving even a single equation of higher degree are quite limited.
Systems of equations will reappear frequently in Algebra 3-4. They will be used in maximization and minimization problems, where solving by graphing will become especially useful. Systems of equations also appear in chemistry and physics; in fact, they are found in any situation dealing with multiple variables and multiple constraints on them.
LINK TO ADDITIONAL Linear Programming Example
(Click above)
Systems of equations will reappear frequently in Algebra 3-4. They will be used in maximization and minimization problems, where solving by graphing will become especially useful. Systems of equations also appear in chemistry and physics; in fact, they are found in any situation dealing with multiple variables and multiple constraints on them.
LINK TO ADDITIONAL Linear Programming Example
(Click above)
Video#1: "Solving Linear Systems by Substitution" (One Example)
Video#2: "Solving Systems of Equations by Elimination" (a few examples)
Video#3: "All I Do Is Solve" School-Made Rap Song Summarizing Systems
Video#4: Solving Linear Programming Word Problems (1 Example)
Videos #5/6: Two Part Video on Linear Programming Word Problem
(You will want to "full screen"these to watch the details better)
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