Methods of Solving Linear Equations and Variations
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Methods of Solving Systems of Linear Equations and Variations
There are countless ways to solve systems of linear equations and variations. The first that come to mind are Substitution, Graphing, and Elimination. There are, however many more methods, such as Row Echelon Form and Back Substitution, Reduced Row Echelon Form and Back Substitution, Elementary Row Operation in a Matrix, Gaussian Elimination, Guass-Jordan Elimination, Matrix Inversion, Determinants, and Cramer's Rule. The ones described in detail will be Substitution, Graphing, and Elimination, because they are the simplest and easiest out of the list.
The method that comes to mind first is Elimination. In the method of Elimination, the key step is to obtain for one of the variables, a variation in sign. This means to have one of the x's in one of the equations negative, and the other x positive. The reason for doing this is so that the equations can be added to each other, and one of the variables will be eliminated, hence the name.
The most simplistic algebraic method is definitely Substitution. A solution would be an ordered pair that solves both equations in the system...