Solving Systems of Equations with Elimination

The video tutorial guides viewers through solving a system of equations using the elimination method. It begins with an introduction to the exercise, followed by setting up the problem with two equations. The tutorial then demonstrates how to manipulate the equations to eliminate a variable, solve for the remaining variables, and verify the solutions. The process is explained step-by-step, ensuring a clear understanding of the elimination method.

Why is it beneficial to practice solving systems of equations using elimination?

• It improves problem-solving skills.

• It is a requirement for all math exams.

• It is the only method to solve equations.

• It helps in party planning.

What are the given equations in the problem that need to be solved?

• 6x + 6y = -24 and 5x - 5y = -60

• 6x + 6y = 24 and 5x + 5y = 60

• 6x - 6y = -24 and -5x - 5y = -60

• 6x - 6y = 24 and -5x - 5y = 60

What is the first step in manipulating the equations to eliminate a variable?

• Add the equations directly.

• Subtract one equation from the other.

• Switch the variables in the equations.

• Multiply or divide to simplify the equations.

How do you simplify the first equation 6x - 6y = -24?

• Add 6 to both sides

• Subtract 6 from both sides

• Divide by 6

• Multiply by 6

What is the purpose of dividing the equations by 6 and 5 respectively?

• To change the signs of the variables.

• To make the equations more complex.

• To eliminate the y variable.

• To simplify the equations for easier elimination.

What is the result of adding the simplified equations?

• x = 4

• y = 8

• x + y = 12

• 2x = 16

After finding y, what is the next step to find x?

• Divide y by 2.

• Multiply y by 2.

• Add y to one of the equations.

• Substitute y back into one of the original equations.

What is the value of x after substitution?

• x = 4

• x = 8

• x = -8

• x = -4

How can you verify the solution is correct?

• By graphing the equations.

• By solving another set of equations.

• By using a calculator.

• By checking if the values satisfy both original equations.

What is the final solution for the system of equations?

• x = 4, y = 8

• x = 8, y = 4

• x = -8, y = -4

• x = -4, y = -8