1. Determinants WKST
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3.7a - Cramer's Rule

2. section 4.4 dangjim@gmail.com Revised ©2011
Cramer’s Rule
section 4.4
Revised ©2011
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3.7a - Cramer's Rule

3. For Your Information Named by Gabriel Cramer in 1700’s
Uses determinant to find solution of the system
Revisit the formula of the determinant for 2x2
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3.7a - Cramer's Rule

4. After Death – Before Christ
Recall
Equation of a determinant (NOT THE INVERSE):
After Death – Before Christ
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3.7a - Cramer's Rule

5. Steps Find the determinant To get x:
Write in determinant form (without the equal sign)
REPLACE the x-coordinates with the numbers associated after the equal sign
Divide it by the determinant
To get y:
Same process as x but replace it with the y-coordinate
Write the answer as an ordered pair
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3.7a - Cramer's Rule

6. D = Determinant Equation: Equations To get x: To get y: .
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3.7a - Cramer's Rule

7. What is the determinant?
Example 1
Use Cramer’s Rule to determine this system:
What is the determinant?
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3.7a - Cramer's Rule

8. First, setup the X solution
Example 1
Use Cramer’s Rule to determine this system:
First, setup the X solution
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3.7a - Cramer's Rule

9. First, setup the X solution
Example 1
Use Cramer’s Rule to determine this system:
First, setup the X solution
To get X, get rid of the coefficients in front of X and replace them with the answers
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3.7a - Cramer's Rule

10. Solve for X. Example 1 Use Cramer’s Rule to determine this system:
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3.7a - Cramer's Rule

11. Solve for X. Example 1 Use Cramer’s Rule to determine this system:
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3.7a - Cramer's Rule

12. Finally, put D in and simplify
Example 1
Use Cramer’s Rule to determine this system:
Finally, put D in and simplify
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3.7a - Cramer's Rule

13. First, setup the Y solution
Example 1
Use Cramer’s Rule to determine this system:
First, setup the Y solution
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3.7a - Cramer's Rule

14. First, setup the Y solution
Example 1
Use Cramer’s Rule to determine this system:
First, setup the Y solution
To get Y, get rid of the coefficients in front of Y and replace them with the answers
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3.7a - Cramer's Rule

15. Solve for Y. Example 1 Use Cramer’s Rule to determine this system:
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3.7a - Cramer's Rule

16. Solve for Y. Example 1 Use Cramer’s Rule to determine this system:
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3.7a - Cramer's Rule

17. Put D in and simplify Example 1
Use Cramer’s Rule to determine this system:
Put D in and simplify
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3.7a - Cramer's Rule

18. Example 1 Use Cramer’s Rule to determine this system:
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3.7a - Cramer's Rule

19. Example 2 Use Cramer’s Rule to determine this system:
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3.7a - Cramer's Rule

20. Your Turn Use Cramer’s Rule to determine this system:
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3.7a - Cramer's Rule

21. Special Occurrences No Solution: Infinite Number of Solutions:
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3.7a - Cramer's Rule

22. Example 3 Use Cramer’s Rule to determine this system:
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3.7a - Cramer's Rule

23. Your Turn Use Cramer’s Rule to determine this system:
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3.7a - Cramer's Rule

24. Example 4
On Monday, Angela babysat for 4 hours, did yard work for 2 hours, and earned a total of $41. On Friday, she babysat for 5 hours, did yard work for 3 hours, and earned a total of $65. Use Cramer’s Rule to determine the hourly rate for each activity.
x = babysitting, y = yard work
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3.7a - Cramer's Rule

25. Example 4
On Monday, Angela babysat for 4 hours, did yard work for 2 hours, and earned a total of $41. On Friday, she babysat for 5 hours, did yard work for 3 hours, and earned a total of $65. Use Cramer’s Rule to determine the hourly rate for each activity.
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3.7a - Cramer's Rule

26. Example 5 4p + 4c + 9f = 3400 p + c + f = 680 4c = 1700
A nutritionist creates a diet for a long-distance runner that includes 3400 Calories from 680 grams of food, with half the Calories coming from carbohydrates. How many grams of protein, carbohydrates, and fat will this diet include?
4p + 4c + 9f = 3400
Equation for total Calories
p + c + f = 680
Total grams of food
4c = 1700
Calories from carbohydrates,
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3.7a - Cramer's Rule

27. Example 5
A nutritionist creates a diet for a long-distance runner that includes 3400 Calories from 680 grams of food, with half the Calories coming from carbohydrates. How many grams of protein, carbohydrates, and fat will this diet include?
p = 119
c = 725
f = 136
The diet includes 119 grams of protein, 425 grams of carbohydrates, and 136 grams of fat.
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3.7a - Cramer's Rule

28. Assignment
Cramer’s Rule WKST
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3.7a - Cramer's Rule