Elimination Method in Linear Systems

The video tutorial covers various methods for solving linear systems, including graphing, substitution, and elimination. It begins with an overview of these methods and then delves into detailed explanations and examples of each. The elimination method is introduced as a new technique, with step-by-step guidance on how to apply it to solve equations. The tutorial also addresses more complex problems and emphasizes the importance of checking solutions for accuracy.

Which method involves finding the point of intersection of two lines?

• Substitution

• Graphing

• Elimination

• Matrix Method

When is the substitution method most effective?

• When both equations are solved for Y

• When one equation is solved for a variable

• When equations have opposite coefficients

• When graphing is not possible

What is the first step in the elimination method?

• Solve for one variable

• Graph the equations

• Make coefficients of one variable opposite

• Substitute one equation into another

In the elimination method, what happens when you add two equations with opposite coefficients?

• The equations become identical

• The variable is eliminated

• The coefficients double

• The solution is found

How can you make coefficients opposite in the elimination method?

• By dividing the equations

• By subtracting the equations

• By multiplying one or both equations

• By adding a constant

What should you do if neither variable has opposite coefficients in elimination?

• Add a constant to one equation

• Use substitution instead

• Graph the equations

• Multiply the equations to create opposite coefficients

Why is a fraction answer more accurate than a decimal?

• Fractions are easier to calculate

• Decimals are always rounded

• Fractions are exact and not rounded

• Decimals are less common

How can you verify the solution of a linear system?

• By checking the coefficients

• By graphing the solution

• By substituting the solution back into the original equations

• By using a calculator

What is the result of adding two equations in the elimination method?

• A graph of the system

• A new equation with one variable

• An equation with no variables

• A solution to the system

What is a good way to check your solution besides using elimination?

• Using a calculator

• Graphing or substitution

• Rewriting the equations

• Guessing the solution