Chapter 2.2: Gauss-Jordan EliminationUnique Solutions•While 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?