Cramer's Rule and Systems of Equations

The video tutorial explains how to solve a system of equations using Cramer's Rule. It begins by converting the system into a matrix equation, then calculates the determinants needed for the solution. The tutorial demonstrates how to find the determinants D, Dx, and Dy, and uses these to solve for x and y. Finally, the solution is verified graphically by showing the point of intersection of the equations on a coordinate plane.

What is the first step in solving a system using Cramer's Rule?

• Graph the equations

• Write the system as a matrix equation

• Find the inverse of the matrix

• Substitute values into the equations

In the matrix setup, what does the first column of the coefficient matrix represent?

• Variable terms

• Coefficients of y

• Coefficients of x

• Constant terms

What is the determinant D of the coefficient matrix?

• -3

• 8

• 12

• 5

How is D sub x calculated?

• By adding the constant terms

• By replacing x coefficients with constant terms

• By subtracting the constant terms

• By replacing y coefficients with constant terms

What is the value of D sub y?

• 24

• -3

• 36

• 12

How do you find the value of x in the system?

• Divide D sub x by D

• Multiply D sub x by D

• Add D sub x and D

• Divide D by D sub x

What is the solution for y in the system?

• 4

• -4

• 1

• -1

What is the ordered pair solution for the system?

• (1, 4)

• (-1, -4)

• (1, -4)

• (-1, 4)

What is the purpose of graphically verifying the solution?

• To determine the y-intercept

• To calculate the area under the curve

• To check the point of intersection

• To find the slope of the lines

What is the point of intersection of the two lines?

• (2, -3)

• (-1, 4)

• (0, 0)

• (1, -4)