Solving Systems of Equations with the Elimination Method

This video tutorial covers the elimination method for solving systems of equations. It begins with an introduction to the method, followed by basic and complex examples. The video also explores special cases where systems have no solution or infinitely many solutions. Finally, it summarizes the method and suggests practice problems.

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

• To eliminate all variables at once

• To combine two equations into one that contains only one variable

• To graphically determine the solution

• To substitute one equation into another

What is a legal operation in the process of elimination?

• Subtracting one variable from another

• Multiplying an equation by a variable

• Dividing one equation by another

• Adding two equations together

When adding two equations, what happens if the coefficients of one variable are exact opposites?

• The variable gets doubled

• The equations become inconsistent

• The variable remains unchanged

• The variable gets eliminated

What is the result of adding two equations where one variable has opposite coefficients?

• The coefficients become doubled

• The equations become undefined

• A new variable is introduced

• The variable with opposite coefficients is eliminated

In the context of solving systems of equations, what does 'elimination' specifically refer to?

• Canceling out equations entirely

• Getting rid of one variable to simplify solving the system

• Removing all variables from an equation

• Eliminating the need for graphing

What can be done if direct addition of two equations does not eliminate a variable?

• Graph the equations to find a solution

• Substitute variables instead of adding

• Divide one equation by the other

• Multiply one or both equations by a constant

How can you force a variable to cancel when adding two equations?

• By subtracting the equations

• By adding a constant to one equation

• By multiplying one or both equations by suitable constants

• By dividing one equation by the other

What does it indicate if, after eliminating a variable, the resulting equation allows solving for the remaining variable?

• The system has infinitely many solutions

• The method was applied incorrectly

• The system has exactly one solution

• The system has no solution

What indicates that a system of equations has no solution?

• When the equations are identical

• When the result is a true statement like 0=0

• When the result is an inconsistent equation like 0=8

• When the variables do not cancel out

What does it mean when both variables are eliminated and you get a true statement?

• The equations are inconsistent

• The system has no solution

• The system has exactly one solution

• The system has infinitely many solutions