Three Variable System of Equations

What is the elimination method used for in solving a 3 variable system of equations?

• To eliminate all variables at once.

• To eliminate one variable at a time

• To introduce new variables.

• To rearrange the equations.

How does the graphical method help in solving a 3 variable system of equations?

• By rearranging the equations to isolate one variable at a time.

• By representing the equations as lines on a graph and finding the point of intersection.

• By using matrix operations to solve the system of equations.

• By substituting values into the equations and solving for the variables.

How many equations are needed to solve a 3 variable system using the graphical method?

• 4

• 1

• 2

• 3

Solve the system.

• (1, 2, -2)

• (1, -3, -2)

• (-1, 3, 2)

• No Solution

Solve the system.

• (3, -2, 4)

• (2, -3, 1)

• (-3, 2, -1)

• Infinitely many solutions

Solve the system. 

• (5, -6, 3)

• (2, 3, -1)

• (-4, 2, 5)

• No Solution

Solve the system.

• (2, -2, 3)

• (2, 1, 4)

• (-2, 2, -3)

• No Solution

Which method is most suitable when dealing with large systems of equations?

• Matrix inversion

• Substitution method

• Cramer's rule

• Gaussian elimination

What is the final step in the matrix method to find the values of the variables?

• Row reduction

• Gaussian elimination

• Forward substitution

• Back substitution

What is the first step to solve the given system of equations?