Solving Systems of Equations

The video tutorial explains the elimination method for solving systems of equations. It begins with an introduction to the method, followed by a detailed step-by-step process. The tutorial includes examples of consistent and inconsistent systems, demonstrating how to find solutions or identify when no solution exists. An application of the method is shown through a real-world problem comparing phone plans, illustrating the practical use of elimination in decision-making.

What is the primary goal of the elimination method when solving systems of equations?

• To graph the equations and find the intersection point

• To multiply equations by a constant

• To substitute one equation into another

• To eliminate one variable by adding or subtracting equations

In the example provided, what is the value of X after eliminating the Y terms?

• X = 3

• X = 5

• X = 7

• X = 1

What is the next step after finding the value of one variable in the elimination method?

• Graph the equations

• Substitute the value back into one of the original equations

• Check for consistency

• Multiply the equations by a constant

What is the first step in the general process of the elimination method?

• Add the equations together

• Multiply one or both equations to align coefficients

• Check for consistency

• Solve for one variable

What does it mean if the result of adding two equations is a false statement like 0 = 3?

• The system is inconsistent and has no solution

• The system has a unique solution

• The system has infinite solutions

• The system is dependent

In the application example, what is the fixed cost for Plan A?

• $10

• $0

• $5

• $8

How much does Plan B charge per minute?

• 10 cents

• 8 cents

• 5 cents

• 12 cents

What is the equation used to find when the two phone plans cost the same?

• 0.08X = 0.12X + 5

• 0.08X + 5 = 0.12X

• 0.12X + 5 = 0.08X

• 0.12X = 0.08X + 5

What is the solution for the number of minutes when both phone plans cost the same?

• 200 minutes

• 125 minutes

• 150 minutes

• 100 minutes

What is the main advantage of using the elimination method over graphing?

• It is easier to understand

• It is faster

• It is more accurate

• It requires less calculation