# System of Equations : Software Techniques and an Example

1. Many free software mathematics packages on the Internet will solve a system of equations given the coefficients in the system.

Problem: find out which of the four techniques (the Method of Addition, the Method of Substitution, Gauss-Jordan Elimination, and Cramer's Rule) is used in the majority of these types of software packages. Give your opinion why this technique is the one most commonly used. I am not sure about this one.

2. Three foods have the following nutritional content per ounce.

Calories, Protein (in grams), Vitamin C (in milligrams)

Food A 40calories,5 protein grams,30vitamin C in miligrams

Food B 200calories,2 protein grams,10 vitaminC in miligrams

Food C 400calories,4 protien grams,300 vitaminCinmiligrams

If a meal consisting of the three foods allows exactly 660 calories, 25 grams of protein, and 425 milligrams of vitamin C, how many ounces of each kind of food should be used?

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#### Solution Preview

(1)Technique used most of the times is Method of Addition. This is because this technique provides a very easy way to eliminate variables. Suppose you have two linear equations in x and y. One can just calculate the ratio of coefficients for one of the variables. Multiply this ratio to the ...

#### Solution Summary

Techniques used by software pakages for the solution os systems of equations are discussed. An example is solved.