Addition Method for Solving Systems

This video tutorial explains how to solve systems of linear equations using the addition method, also known as the elimination method. The method involves adding two equations to eliminate one variable, allowing for the solution of the other. The tutorial includes multiple examples, demonstrating the process of aligning variables, determining which to eliminate, and verifying solutions. The video emphasizes the importance of making coefficients opposites to facilitate elimination and provides step-by-step guidance for solving complex systems.

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

• To graph the equations and find the intersection

• To substitute values directly into the equations

• To eliminate one variable by adding equations

• To find the determinant of the matrix

In the first example, what happens to the Y terms when the equations are added?

• They double in value

• They become negative

• They are eliminated

• They remain unchanged

What is the first step in solving a system using the addition method?

• Substitute values into the equations

• Find the inverse of the matrix

• Line up the variables vertically

• Graph the equations

In the second example, why is it beneficial to eliminate the X terms instead of the Y terms?

• It requires multiplying only one equation

• It is the only possible method

• It results in a simpler equation

• It avoids negative coefficients

What is the result of adding the equations in the second example after making the coefficients opposites?

• A new equation with only Y terms

• A new equation with only X terms

• A new equation with both X and Y terms

• A new equation with no variables

In the third example, what is the least common multiple used to eliminate the Y terms?

• 5

• 10

• 15

• 20

How is the solution verified in the third example?

• By using a calculator

• By calculating the determinant

• By checking the graph of the equations

• By substituting the solution back into the original equations

What is the ordered pair solution for the third example?

• (-3, 1)

• (7, 4)

• (-1, 5)

• (8, -6)

What is emphasized in the conclusion about the addition method?

• The importance of graphing

• The need for complex calculations

• The importance of verifying the solution

• The necessity of using a calculator

What is the key advantage of using the addition method?

• It is faster than substitution

• It requires no calculations

• It always results in integer solutions

• It simplifies the process of solving for one variable