1. Warm up

2. Solving Systems Using Inverse Matrices

3. Systems to Matrices A system of equations in standard form (Ax+By=C) can be written in matrix form [A][X]=[B] Where A are the coefficients, X are the variables and B are the constants.

4. Example 1

5. Example 2: you try

6. Answer

7. Now go the other way

8. Recall…. 1.A matrix multiplied by the identity results in the original matrix 2.A matrix multiplied by its inverse gives you the identity.

9. Now we will want to solve systems using matrices This means solving for x and y. To do this we will multiply both sides of the equation by the inverse matrix.

10. Why this works (proof) No need to write this down, this is for those who are curious….

11. Steps

12. Example Solve this system using inverse matrices.

13. Solution –Step 1 First rewrite the second equation in standard form.

14. Solution- Step 2 Write in Matrix form

15. Solution – step 3 Find inverse on the calculator

16. Solution- step 4

17. Solution – step 5 Write answer in matrix from

18. You try: with three variables! c represents the price of a candy bar d represents the price of a drink p represents the price of popcorn Find the price of all three items.

19. Answer

20. Homework Worksheet – All problems http://teachers.henrico.k12.va.us/math/hcpsa lgebra2/Documents/4-6/4_6HW.pdf http://teachers.henrico.k12.va.us/math/hcpsa lgebra2/Documents/4-6/4_6HW.pdf