Cramer's Rule and Systems of Equations

This video tutorial explains how to solve a system of three linear equations with three unknowns using Cramer's Rule. It covers the importance of having equations in standard form, identifies coefficients and constants, and demonstrates the application of Cramer's Rule. The tutorial also provides guidance on using calculators to compute determinants and interprets the results to find the solution to the system of equations.

What is the primary method used by Cramer's Rule to solve a system of equations?

• Substitution

• Elimination

• Graphing

• Determinants

In Cramer's Rule, what do the 'As', 'Bs', and 'Cs' represent in the equations?

• Constants

• Coefficients of X, Y, and Z

• Variables

• Solutions

When setting up the determinant for X, which column is replaced with constants?

• None

• Third column

• Second column

• First column

What is the purpose of forming matrices A, B, C, and D in the calculation process?

• To simplify the equations

• To organize the coefficients and constants for determinant calculation

• To find the inverse of the system

• To graph the equations

What is the denominator value for X, Y, and Z in the given system of equations?

• 28

• 14

• 84

• 112

What is the solution for X in the system of equations?

• 3

• 2

• 1

• 1/2

What is the solution for Y in the system of equations?

• -4

• -3

• -2

• -1

What is the solution for Z in the system of equations?

• 1

• 3

• 2

• 4

What type of system is indicated by having a single solution?

• Overdetermined

• Consistent and Independent

• Dependent

• Inconsistent

How can the solution to the system of equations be expressed?

• As an ordered triple

• As a pair of numbers

• As a single number

• As a matrix