Exploring Systems of Linear Equations in Algebra II

This video tutorial by Kirk Weiler covers systems of linear equations, starting with a review of two-by-two systems using substitution and elimination methods. It then progresses to solving three-by-three systems, providing detailed explanations and practice problems. The lesson concludes with insights into the broader applications of linear algebra.

What is the first step in solving a system of equations by substitution?

• Substitute one equation into the other

• Multiply both equations by a constant

• Add the equations together

• Divide both equations by a constant

In the substitution method, what should you do if neither equation is solved for a variable?

• Divide both equations by a constant

• Multiply both equations by a constant

• Solve one of the equations for a variable

• Add the equations together

What is the main goal of the elimination method?

• To divide both equations by a constant

• To add the equations together

• To eliminate one of the variables

• To multiply both equations by a constant

When using the elimination method, what should you do if adding the equations does not eliminate a variable?

• Add a different pair of equations

• Multiply one or both equations by a constant

• Subtract one equation from the other

• Divide both equations by a constant

In a 3x3 system, what is the first step after writing down the equations?

• Eliminate one variable from two pairs of equations

• Divide all equations by a constant

• Multiply all equations by a constant

• Add all three equations together

What is the purpose of creating a new 2x2 system from a 3x3 system?

• To solve for one variable

• To simplify the equations

• To eliminate all variables

• To make the system easier to solve

When solving a 3x3 system, why is it important to eliminate the same variable from two pairs of equations?

• To ensure the equations are balanced

• To reduce the number of variables

• To simplify the arithmetic

• To create a consistent system

What should you do if you make a mistake while solving a 3x3 system?

• Ask for help

• Ignore the mistake and continue

• Check your work and correct the mistake

• Start over from the beginning

In the final step of solving a 3x3 system, what is the purpose of back substitution?

• To simplify the equations

• To eliminate any remaining variables

• To find the values of all variables

• To verify the solution

What is a common mistake to avoid when solving a 3x3 system?

• Dividing by zero

• Adding the same equation twice

• Eliminating different variables in different pairs of equations

• Forgetting to multiply both sides of an equation