Exploring Adding and Subtracting Rational Expressions

The video tutorial covers the elimination method for solving equations, focusing on creating opposite coefficients when none are present. It provides step-by-step solutions to example problems, demonstrating how to manipulate equations to find solutions. The tutorial emphasizes the importance of writing answers as ordered pairs and offers multiple examples to reinforce the concepts.

What is the first step in the elimination method when opposite coefficients are not present?

• Add the equations directly

• Subtract one equation from the other

• Divide the coefficients

• Multiply one or both equations to create opposite coefficients

What do you do if the coefficients of the variables are not opposites?

• Leave them as is

• Only add the equations

• Multiply the equations to make the coefficients opposites

• Divide the equations

After adjusting coefficients, what operation is performed to simplify the equations?

• Multiplication

• Division

• Addition

• Subtraction

How is the value of 'y' determined in the elimination method?

• By setting the equations equal to each other

• By graphing the equations

• By adding the modified equations

• By subtracting one equation from the other

How do you find the value of 'x' once 'y' is known?

• Add the equations

• Multiply by the coefficient of x

• Substitute y and solve for x

• None of the above

What should you do after finding the value of one variable?

• Stop the calculation

• Check the solution by plugging it back into the original equations

• Start over with new equations

• None of the above

What is necessary to solve for two variables using elimination?

• The same coefficients for both variables

• None of the above

• Opposite coefficients for one of the variables

• Elimination of both variables

In the context of the elimination method, what does 'opposite coefficients' refer to?

• Coefficients that are completely different

• Coefficients that are both negative

• Coefficients that are both positive

• Coefficients that are numerically equal but have different signs

What is the final step in solving equations using the elimination method?

• Add the two equations

• Graph the equations

• Substitute the known value into any equation to find the other variable

• Multiply the remaining variable by its coefficient

What is the result of solving the equations after finding opposites and adding them?

• A new equation with one variable

• An inequality

• Two separate equations

• A graph