1. Thursday Check Out calculator if you don’t have one.

2. Warm-up Solve this system of equations by the Elimination method, then graphing

3. Section 3-4: Solving Systems of Equations with Matrices Pages 178- 185

4. Objectives I can solve systems of linear equations containing 3 variables using matrices I can write matrix equations from a system of linear equations I can solve for word problems with matrices

5. Matrix Equations Must have all variables in the same order and all to the left of the equation sign. The constant number must be to the right of the equation sign. ALWAYS double check this part of the problem.

6. Matrix Vocabulary Every matrix is made up of N – rows and M- columns. So is called a N x M matrix Common matrices are 2x2, 3x3, 2x1, and 3x1 for this section; however can be as large as you like. The following matrix is 3x3 because it has 3 rows and 3 columns

7. What Size? 2 X 2 3 X 1

8. What Size? 4 X 2 2 X 1

9. Converting Equations into Matrices Given the following linear equations: 7x + 5y = 3 3x – 2y = 22 We will make 3 matrices to make the Matrix Equation: Matrix A Matrix B

10. Example 2: Matrix Equations Given these equations, write a matrix equation: 3x + 4y + 2z = -9 3y – 5z = 12 2x – y = 5 Anytime a variable is missing, put a ZERO for its place. It’s always best to rewrite the equations with all terms before writing the matrix equation. 3x + 4y + 2z = -9 0x + 3y – 5z = 12 2x –1y + 0z = 5

11. Systems of Equations with 3 Variables The solution is always a triple ordered pair (x, y, z). You may again have one solution, no solutions, or infinite solutions.

12. Example: Solving the Matrix Equation Matrix AMatrix B

14. MATRIX MODE

15. Arrow over to EDIT

16. With [A] selected hit ENTER

17. Type in Matrix [A] Dimensions 2 x 2, then ENTER

18. Enter the data for Matrix [A]

19. GO back to MATRIX MODE

20. Arrow over to EDIT and DOWN to Matrix [B]

21. Hit ENTER and then Matrix [B] size 2 x 1, then ENTER

22. Type in data for Matrix [B], then 2 nd MODE (quit)

25. Now ENTER to find solution Solution is: (-3, 7)

26. Your turn (1, 6, -2)

27. Limitations No Solution and Infinite Solutions Matrices will NOT solve You get an Error Message “Singular Matrix” You will have to look at slopes and y- intercepts

28. Word Problems Highlight the key information Assign variables to represent the unknown values Write equation to reflect the data.

29. Problem #1 You have two jobs. One as a lifeguard and one as a cashier. Your lifeguard job pays $8 per hour and cashier pays $6 per hour. Last week you worked a total of 14 hours between the two jobs and earned $96. How many hours did you work at each job?

30. Problem #1 Solution You have two jobs. One as a lifeguard and one as a cashier. Your lifeguard job pays $8 per hour and cashier pays $6 per hour. Last week you worked a total of 14 hours between the two jobs and earned $96. How many hours did you work at each job? Assign variables: L – Hours at lifeguard; C – hours at cashier Now write equations: L + C = 14 8L + 6C = 96 Solution: (6, 8)

31. Problem #2 During a single calendar year, a state trooper issued 375 citations for warnings and speeding violations. There were 37 more warnings than speeding violations. How many of each citation were issued?

32. Problem #2 Solution During a single calendar year, a state trooper issued 375 citations for warnings and speeding violations. There were 37 more warnings than speeding violations. How many of each citation were issued? Assign variables: W – # of warnings; S - # of speeding Now write equations: W + S = 375 W = S + 37 Solution: (206, 169)

33. Problem #3 At a pizza shop, two small pizzas, a liter of soda, and a salad cost $14; one small pizza, a liter of soda, and three salads cost $15; and three small pizzas and a liter of soda cost $16. What is the cost of each item sold separately?

34. Problem #3 Solution At a pizza shop, two small pizzas, a liter of soda, and a salad cost $14; one small pizza, a liter of soda, and three salads cost $15; and three small pizzas and a liter of soda cost $16. What is the cost of each item sold separately? Assign variables: P – small pizza; L – liter of soda; S- salad Now write equations: 2P + 1L + 1S = 14 1P + 1L + 3S = 15 3P + 1L = 16 Solution: (5, 1, 3)

35. Homework Matrix Worksheet Don’t forget, ONE wrong keypunch and you get the wrong answer!! Watch out for Negative Numbers!