Precalculus PreAP/Dual, Revised ©2015 Cramer’s Rule Section 8.5 Precalculus PreAP/Dual, Revised ©2015 Viet.dang@humble.k12.tx.us 12/5/2018 12:11 AM 8.5: Cramer’s Rule

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 12/5/2018 12:11 AM 8.5: Cramer’s Rule

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 12/5/2018 12:11 AM 8.5: Cramer’s Rule

Example 1 Use Cramer’s Rule to determine this system, 𝟒𝒙−𝟐𝒚=𝟏𝟎 𝟑𝒙−𝟓𝒚=𝟏𝟏 What is the determinant? 12/5/2018 12:11 AM 8.5: Cramer’s Rule

Example 1 Use Cramer’s Rule to determine this system, 𝟒𝒙−𝟐𝒚=𝟏𝟎 𝟑𝒙−𝟓𝒚=𝟏𝟏 Setup the 𝒙 solution 12/5/2018 12:11 AM 8.5: Cramer’s Rule

Example 1 Use Cramer’s Rule to determine this system, 𝟒𝒙−𝟐𝒚=𝟏𝟎 𝟑𝒙−𝟓𝒚=𝟏𝟏 Solve 12/5/2018 12:11 AM 8.5: Cramer’s Rule

Example 1 Use Cramer’s Rule to determine this system, 𝟒𝒙−𝟐𝒚=𝟏𝟎 𝟑𝒙−𝟓𝒚=𝟏𝟏 Setup the 𝒚 solution 12/5/2018 12:11 AM 8.5: Cramer’s Rule

Example 1 Use Cramer’s Rule to determine this system, 𝟒𝒙−𝟐𝒚=𝟏𝟎 𝟑𝒙−𝟓𝒚=𝟏𝟏 Solve 12/5/2018 12:11 AM 8.5: Cramer’s Rule

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

Your Turn Use Cramer’s Rule to determine this system, 𝟖𝒙+𝟓𝒚=𝟐 𝟐𝒙−𝟒𝒚=−𝟏𝟎 12/5/2018 12:11 AM 8.5: Cramer’s Rule

Example 3 Use Cramer’s Rule to determine this system, 𝟐𝒙+𝟑𝒚=𝟑𝟓 𝟒𝒙+𝟔𝒚=𝟕𝟓 12/5/2018 12:11 AM 8.5: Cramer’s Rule

Example 4 Use Cramer’s Rule to determine this system, 𝒙−𝟐𝒚=−𝟏𝟎 𝒚=𝟓+ 𝟏 𝟐 𝒙 12/5/2018 12:11 AM 8.5: Cramer’s Rule

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? 12/5/2018 12:11 AM 8.5: Cramer’s Rule

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 12/5/2018 12:11 AM 8.5: Cramer’s Rule

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 12/5/2018 12:11 AM 8.5: Cramer’s Rule

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 12/5/2018 12:11 AM 8.5: Cramer’s Rule

Example 6 Use Cramer’s Rule to determine this system, 𝟑𝒙−𝒚+𝟐𝒛=𝟏𝟖 −𝒙+𝟒𝒚−𝟑𝒛=𝟏 𝟐𝒙 +𝟕𝒛=−𝟓 12/5/2018 12:11 AM 8.5: Cramer’s Rule

Your Turn Use Cramer’s Rule to determine this system, 𝟒𝒙−𝒚+𝒛=𝟏𝟐 𝟐𝒙+𝟐𝒚+𝟑𝒛=𝟏 𝟓𝒙−𝟐𝒚+𝟔𝒛=𝟐𝟐 12/5/2018 12:11 AM 8.5: Cramer’s Rule

Assignment Worksheet 12/5/2018 12:11 AM 8.5: Cramer’s Rule