Cramer's Rule and Systems of Equations

This video tutorial introduces Cramer's Rule, a method for solving systems of equations using determinants. It covers solving systems with two equations and two unknowns, as well as three equations and three variables. The tutorial provides step-by-step examples and demonstrates how to use a graphing calculator to simplify calculations. Cramer's Rule is shown to be an effective method for solving equations, especially when technology is available.

What is the primary mathematical tool used in Cramer's Rule to solve systems of equations?

• Vectors

• Matrices

• Integrals

• Determinants

In a system of two equations, what do the coefficients of the x and y terms form in Cramer's Rule?

• A matrix

• A polynomial

• A determinant

• A vector

When solving for x in a system of two equations using Cramer's Rule, what is replaced in the determinant?

• Both x and y coefficients

• Y coefficients

• X coefficients

• Constants

What is the solution for x in the example of two equations provided in the video?

• x = 0

• x = 3

• x = 1

• x = 2

What remains the same in the pattern when solving a system of three equations using Cramer's Rule?

• The numerators

• The denominators

• The constants

• The coefficients

In a system of three equations, what is replaced to find the numerator for y using Cramer's Rule?

• Z coefficients

• Y coefficients

• Constant terms

• X coefficients

What is the value of the denominator when solving the example of three equations using a graphing calculator?

• 8

• 7

• 6

• 5

What is the solution for y in the example of three equations provided in the video?

• y = -3

• y = -2

• y = -4

• y = -1

Which matrix operation is used to find the numerators in the example of three equations?

• Matrix addition

• Matrix subtraction

• Matrix multiplication

• Matrix determinant

What is the final solution for z in the example of three equations?

• z = 3

• z = 2

• z = 1

• z = 4