Subject: Solving Systems of Linear Equations using Matrices and Matrix Equations

Alex is planning to have a snack during his break from class. He needs to eat 8 grams of fiber and 12 grams of protein. In the vending machine, he finds three types of packaged snacks: crackers that have 1 g of fiber and 2 g of protein, cookies that have 1 g of fiber and 1 g of protein, and nuts that have 3 g of fiber and 4 g of protein. How many of each snack can he eat to obtain his goal?

a. Determine what the variables represent:

x=

y=

z=

b. Write the system of linear equations:

c. Write the Augmented Matrix for the system of linear equations then solve using the Gauss-Jordan Elimination Method. Show the 3 row operations and at least 4 of the resulting matrices. Use proper notation.

d. Fill out the table to show the possible combination of packages of snacks Alex can eat to obtain his goal:

x y z

e. Write the solutions in terms of what the variables represent: