Elimination Method in Systems of Equations

The video tutorial explains the elimination method for solving systems of equations. It begins by identifying which variable to eliminate, then demonstrates how to make the coefficients of the chosen variable opposite in sign by multiplying by negative one. The tutorial proceeds to combine the equations to solve for one variable, Y, and then substitutes back to find the value of the other variable, X. The process is clearly illustrated with step-by-step calculations.

What is the first step in the elimination method?

• Add the equations together.

• Identify a variable to eliminate.

• Multiply both equations by the same number.

• Solve for one variable directly.

Why is it beneficial to eliminate a variable in a system of equations?

• It makes the equations more complex.

• It simplifies the system to a single equation.

• It increases the number of variables.

• It allows for more solutions.

How can you make the coefficients of a variable opposite in sign?

• Subtract one equation from the other.

• Multiply one equation by a negative number.

• Divide both equations by the same number.

• Add a constant to both equations.

What is the result of multiplying a number by negative one?

• The number becomes zero.

• The number becomes positive.

• The number's sign is reversed.

• The number doubles.

What happens when you combine the equations after making the coefficients opposite?

• The equations are solved directly.

• A new variable is introduced.

• The equations become identical.

• The variable is eliminated.

What is the value of Y after solving the combined equation?

• Positive 3

• Negative 3

• Zero

• Positive 9

After finding the value of Y, what is the next step?

• Solve for Z.

• Substitute Y into one of the original equations.

• Multiply both equations by Y.

• Add Y to both equations.

What is the final step in the elimination method?

• Add the solutions together.

• Multiply the solution by a constant.

• Verify the solution by substituting back into the original equations.

• Divide the solutions by each other.

What is the value of X after substituting the value of Y?

• Positive 9

• Positive 3

• Negative 9

• Zero