Augmented Matrices and The Gauss-Jordan Method

(Teacher Notes)

An investor has a total of 45 one-ounce ingots, made of either gold or silver, worth $7636.50. The value of a gold ingot is $280.00, and the value of a silver ingot is $4.25. Find g, the number of gold ingots, and s, the number of silver ingots?

(Released TAKS – July 2006)

System of Equations Augmented Matrices

The process used above is called The Gauss-Jordan Elimination Method. This is a systematic way to solve system of equations and is especially helpful when solving very large systems of equations. The first step in using the Gauss-Jordan Elimination Method is to use the system of equations to set up an augmented matrix (a coefficient matrix next to a constant matrix) . For the problems below, set up a system of equations and the corresponding augmented matrix.