1. Pre-Calculus – Chapter 2
Systems of Equations
It’s time to play…
Pre-Calc
Jeopardy

2. When it is your team’s turn, select a category and an amount.
Rules for the Game
When it is your team’s turn, select a category and an amount.
After Mr. Dillon has finished asking the question, any team may buzz in. If you buzz in early, you will not be called on.
If the team that buzzes in answers correctly, they get those points and choose the next category.
If the team answers incorrectly, they lose the points. Mr. Dillon will then re-read the question so the other teams can have a chance to answer. A team is NOT obligated to answer if they do not want to.
There will be a Final Jeopardy question at the end of the game where teams can wager the points they have earned.
Any questions?

3. Solving Systems of Equations
Today’s Categories
Solving Systems of Equations
Matrix Stuff
Augmented Matrices
Linear Inequalities
Linear Programming
The Answer is One

4. Solving Systems Matrix Stuff Augmented Matrices Linear Inequalities
100
200
300
400
500
Linear Inequalities
Linear Programming
The Answer is One
Go to Final Jeopardy

5. This method for solving systems is the most visual way to solve…
100 Points
This method for solving systems is the most visual way to solve…
Graphing
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6. 200 Points
This method for solving systems involves replacing expressions that are equal.
Substitution
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7. This method for solving systems ends with “-limination.”
300 Points
This method for solving systems ends with “-limination.”
Elimination
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8. 400 Points
This method for solving systems of equations works great when you have 3 or more equations and 3 or more variables.
Augmented Matrices
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9. Solve the following system of equations:
500 Points
Solve the following system of equations:
3x – 4y = 360
5x + 2y = 340
(80, -30)
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10. Two matrices are equal if…
100 Points
Two matrices are equal if…
…they have the same dimensions and each corresponding element is equal.
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11. No. You can only add matrices with the same dimensions.
200 Points
Suppose that A is a 3 x 2 matrix and B is 2 x 3 matrix. Can you determine A + B?
No. You can only add matrices with the same dimensions.
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12. 300 Points
Suppose that A is a 3 x 2 matrix and B is 2 x 3 matrix. Can you determine AB?
Yes. The number of columns in the first matrix must equal the number of rows in the second matrix.
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13. 400 Points
Find AB:
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14. 500 Points
Find the inverse:
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15. This is one row operation that can be used to transform a matrix…
100 Points
This is one row operation that can be used to transform a matrix…
Interchange rows.
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16. 200 Points
This is another row operation that can be used to transform a matrix…
Multiply a row by a scalar.
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17. 300 Points
This is yet another row operation that can be used to transform a matrix…
Multiply a row by a scalar and add it to the row (or a multiple of the row) that you are replacing.
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18. 400 Points
When simplifying a matrix, you want this number in the triangular area below the main diagonal.
ZERO
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19. Solve this system using a matrix:
500 Points
Solve this system using a matrix:
x - 2y + z = 7
3x + y – z = 2
2x + 3y + 2z = 7
(2, -1, 3)
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20. 100 Points
Use this type of line for the boundary when the inequality is less than or greater than.
DOTTED LINE
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21. 200 Points
Use this type of line for the boundary when the inequality is less than or equal to or greater than or equal to.
SOLID LINE
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22. Where the shaded parts of each graph overlap.
300 Points
When solving a system of linear inequalities, this is the region of the graph where the solutions are located.
Where the shaded parts of each graph overlap.
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23. 400 Points
This theorem states that the maximum and/or minimum values of a function constrained by a system of inequalities will be located at the vertices of polygonal region bounded by those inequalities.
VERTEX THEOREM
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24. Solve the following system of inequalities: See Mr. Dillon’s Sketch…
500 Points
Solve the following system of inequalities:
y > 2x – 4
y ≤ -x + 5
See Mr. Dillon’s Sketch…
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25. This is the first step in a linear programming problem.
100 Points
This is the first step in a linear programming problem.
Define the Variables
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26. 200 Points This is the second step in a linear programming problem.
Write the constraints in the form of linear inequalities.
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27. 300 Points This is the third step in a linear programming problem.
Graph the inequalities and find the coordinates of the vertices.
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28. 400 Points This is the fourth step in a linear programming problem.
Write a function to be maximized or minimized.
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29. These are the final two steps in a linear programming problem.
500 Points
These are the final two steps in a linear programming problem.
Substitute the ordered pairs to find the values and select the max/min value.
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30. In an identity matrix, this number is found along the main diagonal.
100 Points
In an identity matrix, this number is found along the main diagonal.
ONE
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31. This is the number of “rows” in a row matrix.
200 Points
This is the number of “rows” in a row matrix.
ONE
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32. This is the number of “columns” in a column matrix.
300 Points
This is the number of “columns” in a column matrix.
ONE
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33. Find the determinant of the following matrix:
400 Points
Find the determinant of the following matrix:
ONE
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34. This is “NOW” spelled backwards.
500 Points
This is “NOW” spelled backwards.
“WON”
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35. The category for Final Jeopardy is... Write down your wager now.
LINEAR PROGRAMMING
Write down your wager now.
Here is the question…

36. FINAL JEOPARDY
Open your books to page 95. Solve question #18. You must show work and your final answer is the amount of “maximum revenue.”
Maximum Revenue: $170000

37. Pre-Calculus – Chapter 2 Pre-Calc is fun and easy!
Systems of Equations
And the winner is…
Pre-Calc is fun and easy!