Elimination Method for Systems of Linear Equations

This video tutorial explains how to use the elimination method to solve systems of linear equations. It covers examples with two and three variables, demonstrating step-by-step how to eliminate variables to find solutions. The video begins with a simple two-variable example, progresses to a more complex two-variable system, and concludes with a three-variable system, emphasizing the importance of finding common multiples and systematically eliminating variables.

What is required to solve a system of equations with two variables?

• One equation

• Two equations

• Four equations

• Three equations

What does the elimination method involve when solving systems of equations?

• Factoring equations

• Graphing equations

• Adding or subtracting equations

• Substituting variables

How do you find the least common multiple (LCM) of 4 and 6?

• 12

• 10

• 24

• 18

What is the result of adding equations to eliminate a variable?

• A new equation with three variables

• A new equation with two variables

• No new equation

• A new equation with one variable

What is the first step in solving a system of equations with three variables?

• Eliminate x first

• Eliminate y first

• Combine two equations to eliminate one variable

• Solve for z first

How do you determine which variable to eliminate first in a three-variable system?

• Eliminate z first

• Random choice

• Eliminate the variable that simplifies the equations

• Always eliminate x first

After finding the value of x in a three-variable system, what is the next step?

• Celebrate

• Find the value of y

• Substitute x back into the original equations

• Find the value of z

What is the value of y when solving the system with three variables in the example?

• 2

• 4

• 3

• 1

In the three-variable system example, what is the correct order of solving for the variables?

• x, y, z

• y, z, x

• z, x, y

• x, z, y

What is the final solution for the three-variable system provided in the example?

• (3, 2, 1)

• (2, 1, 3)

• (1, 2, 3)

• (1, 3, 2)