# 4.5 Solving Systems Using Augmented Matrices (Option #2)

```4.5 Solving Systems Using Augmented Matrices (Option #2)
An augmented matrix is a matrix formed from a linear system of equations. It contains
the coefficients in front of the variables as well as an additional column for the constants
on the right of the equal signs. The new column is set apart by a vertical line.
Ex:
Ex: Write the system of linear equations as a matrix equation
x − 4y = 9
−6x + 7y = −2
becomes
Once a matrix is augmented it can be row reduced in your calculator, solving for the
variables x and y.
Steps for finding the reduced row echelon form on a calculator:
1. Define a matrix
a. 2nd, MATRIX
b. Over to EDIT, Enter &amp; type your dimensions
2. Find the reduced row echelon form
a. 2nd, QUIT
b. 2nd, MATRIX over to MATH
c. Down to B: rref(
3. Recall the matrix to row reduce.
Continue with our example from above…
Ex: Use matrices to solve the linear systems below.
a)
4x − y = 10
−7x − 2y = −25
b) 3x − 5y = −26
−x + 2y = 10
6x + y + 2z = 11
c) x − y + z = −5
−x + 4y − z = 14
x − y − 3z = −1
d) 5x + 2y + z = −17
−3x − y = 8
```