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# Systems of Equations in Three Variables

Author: Kristel Sortelli
##### Description:

You will use technology and algebra to solve systems of linear equations in three variables.

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Tutorial

## Using the Calculator:

What do the A and B represent? The letters A and B are capitalized because they refer to matrices. Specifically, A is the coefficient matrix and B is the constant matrix. In addition, X is the variable matrix. No matter which method you use, it’s important to be able to convert back and forth from a system of equations to matrix form.

This is how the matrices would be set up.

1.  Enter the coefficient matrix, A.  Press to create a matrix from scratch or press to access a stored matrix. See the first screen below.  Make sure that Matrix A is set as a 3 x 3.

2.  Press [ ] to find the inverse of matrix A.  See the second screen below.

3.  Enter the constant matrix, B.  Press to create Matrix B.  See the third screen below.  Make sure that Matrix B is set as a 3 x 1.

4.  Press to evaluate the variable matrix, X.  The variable matrix indicates the solutions: x = 5, y = 0, and z = 1. See the third screen below.  Remember that the answers for each variable will go in order - x, y, z.