Elimination Method in Systems of Equations

The video tutorial explains how to solve a system of equations using the method of elimination. It begins by discussing the possible outcomes of solving such systems: one solution, no solution, or infinite solutions. The tutorial then demonstrates graphing the equations as planes in space to find intersections. The method of elimination is used to simplify and solve the equations step-by-step, focusing on eliminating terms and solving for variables. Finally, back substitution is employed to find the remaining variable, resulting in the ordered triple solution.

What are the possible outcomes when solving a system of equations?

• Two solutions, no solution, or infinite solutions

• One solution, two solutions, or infinite solutions

• One solution, two solutions, or no solution

• One solution, no solution, or infinite solutions

What does it mean if the graph of three planes intersects at a single point?

• The system has one solution

• The system has two solutions

• The system has infinite solutions

• The system has no solution

What is the first step in the method of elimination?

• Divide all equations by a constant

• Subtract one equation from another

• Add two equations to eliminate a variable

• Multiply all equations by a constant

When using elimination, what should you do if the terms are already opposites?

• Subtract the equations

• Add the equations directly

• Ignore the equations

• Multiply the equations by a constant

What is the result of adding equations A and B in the elimination process?

• 12x - 8z = 12

• 12x - 7z = 33

• 12x - 8z = 33

• 12x - 7z = 12

How do you find the value of z in the system of equations?

• By solving 12x + 7z = 45

• By solving 12x - 7z = 33

• By solving -15z = 45

• By solving 12x - 8z = 12

What is the value of z in the solution?

• 3

• 1

• -3

• -1

What is the next step after finding the value of z?

• Check the solution by substitution

• Solve for y using substitution

• Solve for x using substitution

• Graph the equations again

What is the value of x in the solution?

• -1

• -3

• 3

• 1

What is the final ordered triple solution of the system?

• (-1, 1, -3)

• (-1, -1, -3)

• (1, -1, 3)

• (1, 1, 3)