Solving Systems of Linear Equations by Elimination

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

• To graph the equations

• To find the y-intercept

• To find the slope of the lines

• To eliminate one of the variables

What is the German term for the elimination method?

• Division Methode

• Multiplikation Methode

• Subtraktion Methode

• Addition Methode

In the elimination method, what is the result when you successfully eliminate a variable?

• A single equation with one variable

• A system with more variables

• An equation with no variables

• A graph of the lines

What is the first step in the elimination method?

• Add the equations directly

• Multiply one or both equations to align coefficients

• Subtract the equations

• Graph the equations

What should you do after finding the values of x and y in a system of equations?

• Calculate the determinant

• Find the slope of the lines

• Verify by substituting back into the original equations

• Graph the solution

How do you verify that a point is a solution to a system of equations?

• By finding the slope

• By checking if it lies on the graph

• By calculating the determinant

• By substituting the point into both equations

When solving a system of equations, why might you choose to eliminate the y variable instead of x?

• To avoid fractions

• If the coefficients of y are already opposites

• Because y is always easier to eliminate

• To simplify the graphing process

In the second example, what was the chosen variable to eliminate?

• x

• y

• Neither

• Both x and y

What does it mean if, after elimination, both variables are eliminated and you get a false statement like 0 = -12?

• The system has infinitely many solutions

• The system has no solution and the lines are parallel

• The system is inconsistent

• The system has a unique solution

What indicates that two lines are parallel when using the elimination method?

• They intersect at one point

• They have different slopes

• They have the same slope but different y-intercepts

• They have the same y-intercept