Understanding Cramer's Rule and Linear Equations

The video tutorial explains how to create and solve a system of linear equations using Cramer's Rule. The problem involves mixing yellow and blue paint to achieve a green color, with constraints on total gallons and cost. The tutorial walks through setting up equations, understanding Cramer's Rule, and applying it to find the number of gallons of each paint color used.

What is the total amount of paint used in the mix?

• 7 gallons

• 8 gallons

• 10 gallons

• 9 gallons

How much does each gallon of yellow paint cost?

• $15

• $19

• $21

• $17

What is the total cost of the paint mix?

• $120

• $125

• $130

• $133

What mathematical tool does Cramer's Rule use to solve systems of equations?

• Integrals

• Matrices

• Determinants

• Vectors

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

• Constants

• Coefficients of y

• Both coefficients of x and y

• Coefficients of x

When solving for x using Cramer's Rule, what is replaced in the determinant?

• First column with constants

• Second column with constants

• Both columns with constants

• No replacement

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

• 17 and 13

• 1 and 17

• 9 and 133

• 1 and 13

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

• 1 times 133 minus 9 times 17

• 9 times 17 minus 1 times 133

• 9 times 13 minus 1 times 133

• 1 times 17 minus 1 times 13

How many gallons of yellow paint are in the final mix?

• 6 gallons

• 5 gallons

• 3 gallons

• 4 gallons

How many gallons of blue paint are in the final mix?

• 6 gallons

• 3 gallons

• 4 gallons

• 5 gallons