Solving Systems of Equations

The video tutorial demonstrates solving a system of three equations with three unknowns using the elimination method. It begins by labeling the equations and proceeds to eliminate the Z variable from pairs of equations to form two equations with two unknowns. The tutorial then solves for X and Y, and finally finds the value of Z through back substitution. The solution is verified as a consistent and independent system, represented as a point of intersection of three planes in space.

What is the first step in solving a system of three equations using elimination?

• Label the equations and eliminate one variable.

• Solve for one variable directly.

• Graph the equations.

• Substitute values into the equations.

When eliminating a variable, what should be done to the coefficients of the variable in the two equations?

• Make them equal.

• Make them opposites.

• Make them zero.

• Make them positive.

After eliminating the Z variable from two pairs of equations, what is the next step?

• Substitute back into the original equations.

• Graph the remaining equations.

• Form two equations with two unknowns.

• Solve for Z directly.

How do you solve the system of two equations with two unknowns?

• By eliminating one of the variables.

• By substituting one equation into the other.

• By guessing the values.

• By graphing the equations.

What is the value of X in the solution to the system?

• 20/57

• 1/4

• 9/20

• 57/20

What is the value of Y in the solution to the system?

• -9/20

• 9/20

• 57/20

• 1/4

What is the value of Z in the solution to the system?

• 9/20

• -9/20

• 57/20

• 1/4

What does the solution to the system of equations represent geometrically?

• A circle in space.

• A line in space.

• A point of intersection of three planes.

• A single plane.

What is the term used to describe a system with exactly one solution?

• Dependent

• Overdetermined

• Consistent and independent

• Inconsistent

What is the importance of visualizing the solution on a graph?

• To check for errors in calculation.

• To understand the geometric interpretation.

• To find more solutions.

• To simplify the equations.