1. 9-4 Determinants and Cramer’s Rule

2. Solving Systems
Solve the Following equation:

3. Cramer’s Rule
Cramer’s Rule is a neat way to evaluate systems and if you put the work in now you’ll do fine. It can be used for any size (2 by 2, 3 by 3 or even larger) system.
It is easy to memorize and fast.

4. Definitions Determinant – a square array
2nd Order Determinant – a 2 by 2 array
3rd Order Determinant – a 3 by 3 array
Elements – The things in the array

5. What does a determinant look like?
A 2nd order determinant looks like this
And the value of the determinant =
Diagonal down right – diagonal up to right ae - bd

6. Examples
Evaluate 1. 2.
9 – 1 = 8
2 – (-12) = 14

7. Why is this useful for systems?
Lets work through an elimination example using all variables; then we can see how the determinant will be useful in solving.
Just follow – you don’t need to write it down.

8. Lets eliminate y
Look familiar?

9. If you apply the same process but eliminate x
So, what does Cramer’s Rule say?

10. Cramer’s Rule Given a system
Replace solutions in y column to solve for y
Replace solutions in x column to solve for x
Denominators are coefficient deterimanants

13. Group Problem
Find the distance between:
y=x-4 and the point (-2,4)