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Linear Equations

             If you are given a system of n or more equations involving n unknowns, we learned there are many different methods to solve the system such as - Elimination, Cramer, Expansion by Minors, and Augmented Matices. .
             Elimination is the process of "eliminating" each n unknown or variable. The process begins by picking one of the unknowns, or variable, then finding an equation in which it appears. Elimination works nicely when you have coefficients that are integers and three or less system of equations and unknowns, but as the number of equations and unknowns increases, and fractions come into play, Elimination can be cumbersome and the margin for error widen. .
             You will see in contrast to other methods, that when you have to multiply multiple equations by different constants to get matching coefficients, Elimination starts to seem like more problematic than it's worth and other methods such as Minors and Matrices have an advantage. This is particularly true as the number of equations and variables become larger. Then the other three methods (Cramer, Expansion by Minors, and Augmented Matices) have an advantage. Alot of math and work must be done to reach a solution, but the answers are usually pretty straight forward and solving equations with fractions can be easier. And if computers or certain calculators are available results are quicker.
             In comparison, all of the methods are linear equations that can be used to solve a system of 2 or more equations with n unknowns in a fairly orderly manner.
             other methods of determinants such as Cramer, Expansion by Minors, and Augmented Matices, share a common matrix. .
             With Cramer's method can be used for n unknowns. Alot of multiplication and division are done mixed in with addition making it more difficult. .
             If the values in the system are not relatively close, the system will be .
             open to errors. .
             Expansion by Minors, a higher order determinant, is a technique that can be used for computing small systems.

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