1. Using Determinants to solve systems of equations
4.6 Cramer’s Rule
Using Determinants to solve systems of equations

2. A system of equations can be written as a matrix
3x + 5y
-2x + 7y becomes the matrix
x – 6y + 3z
4y – 8z
5x – 3y becomes
I will call this type of matrix an operation matrix

3. Cramer’s Rule using the determinants of two matrices
5x + 4y = 28 Find the determinant of the
3x – 2y = 8 operation matrix

4. Cramer’s Rule using the determinants of two matrices
5x + 4y = 28 Find the determinant of the
3x – 2y = 8 matrix where one of the variables coefficient are replaced with the answers. When solve for x use
Find it determinant
We will call this the new answer martix

5. Cramer’s Rule using the determinants of two matrices
Now to solve for x divide the new answer matrix by the operation matrix
x is 4; y can be found the same way

6. Matrix for y New answer matrix
Then divide by -22, for the operation matrix

7. Lets solve this system equations by Cramer’s rule
2x – 3y + z = 5
x + 2y + z = -1
x – 3y + 2z = 1
Need to find the determinants of

8. Find the determinant
We will use this for the denominators in the all the fractions.

9. Solve for x
Replace the x column with the answers. So

10. Solve for y
Replace the y column with the answers. So

11. Solve for z
Replace the z column with the answers. So

12. Homework
Page 192 – 193
# 13,15, 17, 21,
23, 27, 29, 31

13. Homework
Page 192 – 193
# 12, 14, 16, 20,
22, 26, 28, 30