**Augmented Matrices and The Gauss-Jordan Meth****od**
(Teacher Notes)
Use the information below to set up a system of equations and then solve the system using the elimination method.
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
*Answer:*
1^{st} : Find *s* by eliminating *g*.
2^{nd} : Find *g* by eliminating *s* in R_{1}.
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.
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