2-2 - Chapter 2.2 Gauss-Jordan Elimination Unique Solutions While the method of substitution works it is somewhat clumsy when we work with equations

2-2 - Chapter 2.2 Gauss-Jordan Elimination Unique Solutions...

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Chapter 2.2: Gauss-Jordan Elimination Unique Solutions While the method of substitution works, it is somewhat clumsy when we work with equations involving three or more variables. We will look at a more methodical way of solving a system of equations, called the Gauss-Jordan Elimination Method . Two systems of equations are equivalent if they have the same solution. With the Gauss-Jordan method, we transform a given system into an simpler equivalent system using three operations: 1. Interchanging equations. 2. Multiplying every term of an equation by a constant. 3. Adding/subtracting two equations. Example: Solve the following system: x + y = 16 8 x + 10 y = 146 Subtract 8 times equation (1) from equation (2): x + y = 16 2 y = 18 Multiply equation (2) by 1 2 : x + y = 16 y = 9 Subtract equation (2) from equation (1): x = 7 y = 9 We have solved for x and y , and found one solution to the given system of equations. (Don’t forget to check the solution!) What did I do to find my solution? 1
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