Elimination Method in Systems of Equations

The video tutorial explains how to solve systems of equations using the elimination method. It covers identifying and creating opposite variables, using multiplication to adjust equations, and handling special cases like no solution or infinite solutions. The tutorial provides step-by-step examples to illustrate each concept.

What is the primary goal when using the elimination method to solve systems of equations?

• To find the sum of all variables

• To eliminate one variable by adding opposites

• To multiply all terms by zero

• To divide all terms by the same number

In the context of elimination, what does it mean to have opposite variables?

• Variables that are the same in both magnitude and sign

• Variables that are different in both magnitude and sign

• Variables that are equal in magnitude but opposite in sign

• Variables that are equal in magnitude and sign

In the example with opposite variables, what is the first step after identifying opposite variables?

• Add the equations

• Multiply the equations

• Subtract the equations

• Divide the equations

After eliminating a variable, what is the next step to find the solution in a system of equations?

• Multiply the result by zero

• Substitute the found value into one of the original equations

• Add a new variable

• Divide the result by the number of variables

What is the result of adding two equations with opposite variables?

• The variables remain unchanged

• The variables are doubled

• The variables are eliminated

• The variables are halved

When you do not have exact opposite variables, what can you do to create them?

• Add a constant to both equations

• Divide both equations by the same number

• Multiply one or both equations by a suitable number

• Subtract a constant from both equations

In the example where both equations are multiplied, what indicates that there are infinitely many solutions?

• The equations have different slopes

• The equations result in a true statement like 0 = 0

• The equations result in a false statement

• The equations have no variables left

In the example with infinitely many solutions, what operation is performed on both equations to achieve opposite variables?

• Addition

• Division

• Subtraction

• Multiplication

What is the least common multiple used to create opposite x variables in the final example?

• 25

• 20

• 15

• 10

What conclusion can be drawn if the final result of adding two equations is a false statement like 0 = 13?

• There is one unique solution

• There are infinitely many solutions

• There is no solution

• The solution is undefined