Determinants WKST 12/6/2018 8:55 PM 3.7a - Cramer's Rule

section 4.4 dangjim@gmail.com Revised ©2011 Cramer’s Rule section 4.4 dangjim@gmail.com Revised ©2011 12/6/2018 8:55 PM 3.7a - Cramer's Rule

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 12/6/2018 8:55 PM 3.7a - Cramer's Rule

After Death – Before Christ Recall Equation of a determinant (NOT THE INVERSE): After Death – Before Christ 12/6/2018 8:55 PM 3.7a - 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: Same process as x but replace it with the y-coordinate Write the answer as an ordered pair 12/6/2018 8:55 PM 3.7a - Cramer's Rule

D = Determinant Equation: Equations To get x: To get y: . 12/6/2018 8:55 PM 3.7a - Cramer's Rule

What is the determinant? Example 1 Use Cramer’s Rule to determine this system: What is the determinant? 12/6/2018 8:55 PM 3.7a - Cramer's Rule

First, setup the X solution Example 1 Use Cramer’s Rule to determine this system: First, setup the X solution 12/6/2018 8:55 PM 3.7a - Cramer's Rule

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 12/6/2018 8:55 PM 3.7a - Cramer's Rule

Solve for X. Example 1 Use Cramer’s Rule to determine this system: 12/6/2018 8:55 PM 3.7a - Cramer's Rule

Solve for X. Example 1 Use Cramer’s Rule to determine this system: 12/6/2018 8:55 PM 3.7a - Cramer's Rule

Finally, put D in and simplify Example 1 Use Cramer’s Rule to determine this system: Finally, put D in and simplify 12/6/2018 8:55 PM 3.7a - Cramer's Rule

First, setup the Y solution Example 1 Use Cramer’s Rule to determine this system: First, setup the Y solution 12/6/2018 8:55 PM 3.7a - Cramer's Rule

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 12/6/2018 8:55 PM 3.7a - Cramer's Rule

Solve for Y. Example 1 Use Cramer’s Rule to determine this system: 12/6/2018 8:55 PM 3.7a - Cramer's Rule

Solve for Y. Example 1 Use Cramer’s Rule to determine this system: 12/6/2018 8:55 PM 3.7a - Cramer's Rule

Put D in and simplify Example 1 Use Cramer’s Rule to determine this system: Put D in and simplify 12/6/2018 8:55 PM 3.7a - Cramer's Rule

Example 1 Use Cramer’s Rule to determine this system: 12/6/2018 8:55 PM 3.7a - Cramer's Rule

Example 2 Use Cramer’s Rule to determine this system: 12/6/2018 8:55 PM 3.7a - Cramer's Rule

Your Turn Use Cramer’s Rule to determine this system: 12/6/2018 8:55 PM 3.7a - Cramer's Rule

Special Occurrences No Solution: Infinite Number of Solutions: 12/6/2018 8:55 PM 3.7a - Cramer's Rule

Example 3 Use Cramer’s Rule to determine this system: 12/6/2018 8:55 PM 3.7a - Cramer's Rule

Your Turn Use Cramer’s Rule to determine this system: 12/6/2018 8:55 PM 3.7a - Cramer's Rule

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 12/6/2018 8:55 PM 3.7a - Cramer's Rule

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. 12/6/2018 8:55 PM 3.7a - Cramer's Rule

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, 12/6/2018 8:55 PM 3.7a - Cramer's Rule

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. 12/6/2018 8:55 PM 3.7a - Cramer's Rule

Assignment Cramer’s Rule WKST 12/6/2018 8:55 PM 3.7a - Cramer's Rule