Solving Systems of Three Variables

The video tutorial explains how to solve a system of three equations with three unknowns by using the elimination method. It begins by introducing the concept of intersecting planes in three dimensions. The tutorial then demonstrates how to eliminate the z variable by scaling and adding equations. After reducing the system to two equations with two unknowns, it solves for x and y. Finally, it finds the value of z and verifies that the solution satisfies all original equations.

What is the primary goal when solving a system of three equations with three unknowns?

• To find where three lines intersect in two dimensions

• To determine where three planes intersect in three dimensions

• To calculate the sum of all variables

• To graph the equations on a plane

What method is used initially to solve the system of equations in the video?

• Graphical method

• Substitution method

• Elimination method

• Matrix method

By scaling the third equation by 2, what variable does the teacher aim to eliminate?

• x

• z

• y

• None of the above

What is the result of adding the scaled equations to eliminate z?

• No change in the number of variables

• An equation in x and z

• An equation in y and z

• An equation in x and y

What operation is performed to eliminate y after z has been eliminated?

• Addition of equations

• Subtraction of equations

• Multiplication of one equation

• Division of one equation

What is the value of x found through elimination?

• 2

• 0

• -1

• 1

After finding x, what is the next variable to solve for?

• Both y and z simultaneously

• z

• None, as all variables are solved

• y

What is the final value of y determined through back-substitution?

• -2

• -1

• 2

• 1

What is the value of z calculated in the last steps of the solution?

• -1

• 1

• -4

• 4

How is the solution verified in the video?

• By peer review

• By checking with a calculator

• By graphing the solutions

• By substituting back into the original equations