Understanding Systems of Linear Equations and Cramer's Rule

The video tutorial explains how to create and solve a system of linear equations using Cramer's Rule. The problem involves determining the number of common and rare cards in a collection based on their total value and quantity. The tutorial walks through setting up the equations, applying Cramer's Rule, and calculating determinants to find the solution, concluding with the number of each type of card.

What is the total value of the card collection in dollars?

• $25

• $76

• $162

• $75

If x represents the number of common cards, what does y represent?

• The total value of the collection

• The value of common cards

• The number of rare cards

• The total number of cards

What is the value of each common card in cents?

• 100 cents

• 75 cents

• 25 cents

• 50 cents

What mathematical method is used to solve the system of equations in this problem?

• Gaussian Elimination

• Substitution

• Graphical Method

• Cramer's Rule

In Cramer's Rule, what do the denominators of the determinants represent?

• The constants on the right

• The coefficients of y

• The coefficients of x

• The total number of cards

What is replaced in the numerator determinant when solving for x using Cramer's Rule?

• The total value

• The coefficients of y

• The constants

• The coefficients of x

What are the coefficients of x in the system of equations?

• 1 and 0.75

• 1 and 0.25

• 0.25 and 0.75

• 0.5 and 1

What is the determinant in the numerator for y when using Cramer's Rule?

• 1 times 76 minus 162 times 0.25

• 162 times 0.75 minus 1 times 76

• 1 times 0.75 minus 1 times 0.25

• 76 times 1 minus 0.25 times 162

How many common cards are in the collection?

• 76

• 71

• 91

• 162

How many rare cards are in the collection?

• 76

• 91

• 71

• 162