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

• Notes
• 9

This preview shows page 1 - 5 out of 9 pages.

Chapter 2.2: Gauss-Jordan EliminationUnique SolutionsWhile the method of substitution works, it is somewhat clumsywhen we work with equations involving three or more variables.We will look at a more methodical way of solving a system ofequations, called theGauss-Jordan Elimination Method.Two systems of equations areequivalentif they have the samesolution.With the Gauss-Jordan method, we transform a given systeminto 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=168x+10y=146Subtract 8 times equation (1) from equation (2):x+y=162y=18Multiply equation (2) by12:x+y=16y=9Subtract equation (2) from equation (1):x=7y=9We have solved forxandy, and found one solution to the givensystem of equations. (Don’t forget to check the solution!)What did I do to find my solution?
1
2
3