Systems Of Linear Equations And Problem Solving

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First we started with Graphing Systems of Equations.

Then we moved onto solving systems using the Substitution Method.

For the purposes of this section, we will only use variables to represent the three dimensions.

The conventional arrangement of axes for a graph of a function in three dimensions is shown below.

Although an additional variable (z) is added, the concepts and method of solution are all the same.

Each equation can be graphed using an aspect drawing as a plane.Likewise, we can also solve for the intersection (if it exists) of many linear functions in multiple dimensions by analyzing the associated system of linear equations.A system of linear equations is a set of equations (in some number of variables that may be greater than one or two) that must all be solved simultaneously.The following videos will show four types of linear equations and how to solve each type. You have learned many different strategies for solving systems of equations!In lesson 4, we solved some problems that involved two functions by equating the expressions.Let's briefly look at an example again, but let's write it using our = 3 Solving the system of equations expressed in this manner is essentially the same, but we give it a slight twist.For the sake of certainty, you can also check the solution using the other two equations.Obviously, the substitution method is tedious, and it becomes more so very quickly as the number of variables in the problem increases.We can calculate the intercepts by setting any two of the variables equal to zero.This calculator solves Systems of Linear Equations using Gaussian Elimination Method, Inverse Matrix Method, or Cramer's rule.

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