Solving Systems of Equations Using the Elimination Method

What is the primary goal of the elimination method in solving systems of equations?

• To find the value of one variable first

• To eliminate one variable to simplify solving

• To multiply equations by a constant

• To graph the equations and find the intersection

When aligning equations for elimination, what must be vertically aligned?

• The variables and constants

• Only the variables

• Only the constants

• The equals signs

What is the result of adding two equations where one variable cancels out?

• A graph intersection point

• An undefined equation

• A new system of equations

• A single-variable equation

What do you do if direct addition of equations does not eliminate a variable?

• Subtract the equations instead

• Multiply one equation by a constant

• Graph the equations

• There is no solution

What does 0 = 21 indicate in the context of solving systems of equations by elimination?

• One unique solution exists

• The system has infinitely many solutions

• The equations are identical

• There is no solution

What does it mean if you get 0 = 0 when solving a system of equations by elimination?

• The equations are not linear

• The system has exactly one solution

• The system has no solution

• The system has infinitely many solutions

What is the least common multiple (LCM) used for in the context of the elimination method?

• To decide which variable to eliminate first

• To determine the number of solutions

• To find the best equation to substitute

• To help modify equations so a variable can be eliminated

Why might you need to multiply both equations by a number before adding them in the elimination method?

• To create identical equations

• To ensure the equations have a solution

• To make the coefficients of one variable opposites

• To simplify the equations

After eliminating a variable and solving for the other, what is the next step?

• Graph the solution

• Eliminate the second variable

• There are no further steps

• Check the solution in both original equations

What flexibility does the elimination method offer when solving systems of equations?

• Neither A nor B

• Both A and B

• Choosing between addition and subtraction

• Choosing which variable to eliminate