1. Precalculus PreAP/Dual, Revised ©2015
Cramer’s Rule
Section 8.5
Precalculus PreAP/Dual, Revised ©2015
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8.5: Cramer’s Rule

2. 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:
REPLACE the 𝒚-coordinates with the numbers associated after the equal sign
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8.5: Cramer’s Rule

3. Cramer’s Rule Equations
To solve for 𝒙: 𝒙= 𝑫 𝒙 𝑫
To get 𝒚: 𝒚= 𝑫 𝒚 𝑫
Where 𝑫 is the determinant
𝑫=𝑨𝑫−𝑩𝑪
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8.5: Cramer’s Rule

4. Example 1
Use Cramer’s Rule to determine this system, 𝟒𝒙−𝟐𝒚=𝟏𝟎 𝟑𝒙−𝟓𝒚=𝟏𝟏
What is the determinant?
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8.5: Cramer’s Rule

5. Example 1
Use Cramer’s Rule to determine this system, 𝟒𝒙−𝟐𝒚=𝟏𝟎 𝟑𝒙−𝟓𝒚=𝟏𝟏
Setup the 𝒙 solution
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8.5: Cramer’s Rule

6. Example 1
Use Cramer’s Rule to determine this system, 𝟒𝒙−𝟐𝒚=𝟏𝟎 𝟑𝒙−𝟓𝒚=𝟏𝟏
Solve
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8.5: Cramer’s Rule

7. Example 1
Use Cramer’s Rule to determine this system, 𝟒𝒙−𝟐𝒚=𝟏𝟎 𝟑𝒙−𝟓𝒚=𝟏𝟏
Setup the 𝒚 solution
12/5/ :11 AM
8.5: Cramer’s Rule

8. Example 1
Use Cramer’s Rule to determine this system, 𝟒𝒙−𝟐𝒚=𝟏𝟎 𝟑𝒙−𝟓𝒚=𝟏𝟏
Solve
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8.5: Cramer’s Rule

9. Example 2 Use Cramer’s Rule to determine this system, 𝟑𝒙+𝟒𝒚=𝟏 𝟓𝒙+𝟑𝒚=𝟗

10. Your Turn
Use Cramer’s Rule to determine this system, 𝟖𝒙+𝟓𝒚=𝟐 𝟐𝒙−𝟒𝒚=−𝟏𝟎
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8.5: Cramer’s Rule

11. Example 3
Use Cramer’s Rule to determine this system, 𝟐𝒙+𝟑𝒚=𝟑𝟓 𝟒𝒙+𝟔𝒚=𝟕𝟓
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8.5: Cramer’s Rule

12. Example 4
Use Cramer’s Rule to determine this system, 𝒙−𝟐𝒚=−𝟏𝟎 𝒚=𝟓+ 𝟏 𝟐 𝒙
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8.5: Cramer’s Rule

13. Example 5
Use Cramer’s Rule to determine this system, −𝒙+𝟐𝒚−𝟑𝒛=𝟏 𝟐𝒙 𝒛=𝟎 𝟑𝒙−𝟒𝒚+𝟒𝒛=𝟐
What is the determinant?
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8.5: Cramer’s Rule

14. Example 5
Use Cramer’s Rule to determine this system, −𝒙+𝟐𝒚−𝟑𝒛=𝟏 𝟐𝒙 𝒛=𝟎 𝟑𝒙−𝟒𝒚+𝟒𝒛=𝟐
Setup the 𝒙 solution
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8.5: Cramer’s Rule

15. Example 5
Use Cramer’s Rule to determine this system, −𝒙+𝟐𝒚−𝟑𝒛=𝟏 𝟐𝒙 𝒛=𝟎 𝟑𝒙−𝟒𝒚+𝟒𝒛=𝟐
Setup the 𝒚 solution
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8.5: Cramer’s Rule

16. Example 5
Use Cramer’s Rule to determine this system, −𝒙+𝟐𝒚−𝟑𝒛=𝟏 𝟐𝒙 𝒛=𝟎 𝟑𝒙−𝟒𝒚+𝟒𝒛=𝟐
Setup the 𝒛 solution
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8.5: Cramer’s Rule

17. Example 6
Use Cramer’s Rule to determine this system, 𝟑𝒙−𝒚+𝟐𝒛=𝟏𝟖 −𝒙+𝟒𝒚−𝟑𝒛=𝟏 𝟐𝒙 𝟕𝒛=−𝟓
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8.5: Cramer’s Rule

18. Your Turn
Use Cramer’s Rule to determine this system, 𝟒𝒙−𝒚+𝒛=𝟏𝟐 𝟐𝒙+𝟐𝒚+𝟑𝒛=𝟏 𝟓𝒙−𝟐𝒚+𝟔𝒛=𝟐𝟐
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8.5: Cramer’s Rule

19. Assignment
Worksheet
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8.5: Cramer’s Rule