1. 4-8 Augmented Matrices and Systems

2. Cramer’s Rule System Use the x- and y- coefficients.
Replace the x-coefficient with the constants
Replace the y-coefficient with the constants
The solution of the system is :

3. 7x – 4y = 15 3x + 6y = 8 Use Cramer’s rule to solve the system .
Evaluate three determinants. Then find x and y.
The solution of the system is , 61 27 11 54

4. –2x + 8y + 2z = –3 –6x + 2z = 1 –7x – 5y + z = 2
Find the y-coordinate of the solution of the
system
–2x + 8y + 2z = –3
–6x z = 1
–7x – 5y + z = 2

5. Draw a vertical bar to separate the coefficients from constants.
Write an augmented matrix to represent the
system
–7x + 4y = –3
x + 8y = 9
System of equations
–7x + 4y = –3
x + 8y = 9
x-coefficients
y-coefficients
constants
Augmented matrix
– –3
Draw a vertical bar to separate the coefficients from constants.

6. Write a system of equations for the augmented
matrix
9 –7 –1 –6
Augmented matrix
– –1 –6
x-coefficients
y-coefficients
constants
System of equations
9x – 7y = –1
2x y = –6

7. Use an augmented matrix to solve the system
x – 3y = –17
4x + 2y = 2
1 –3 –17
Write an augmented matrix.
Multiply Row 1 by –4 and add it to Row 2.
Write the new augmented matrix.
1 –3 –17
–4(1 –3 –17) 1 14
1 –3 –17
Multiply Row 2 by
Write the new augmented matrix.
( )

8. (continued)
1 –3 –17
1 –3 –17
3( ) –2
Multiply Row 2 by 3 and add it to Row 1.
Write the final augmented matrix. –2
The solution to the system is (–2, 5).

9. 4x + 3y + z = –1 –2x – 2y + 7z = –10. 3x + y + 5z = 2
Use the rref feature on a graphing calculator to solve the system
4x + 3y + z = –1
–2x – 2y + 7z = –10.
3x + y + 5z = 2
Step 1: Enter the
augmented matrix
as matrix A.
Step 2: Use the rref feature
of your graphing
calculator.
The solution is (7, –9, –2).

10. Homework
Worksheet