Elimination Method in Linear Systems

In this lesson, Mr. Holcomb explains how to solve linear systems using the elimination method. The video covers three examples, each demonstrating different techniques to adjust and eliminate variables. The lesson concludes with an exercise on verifying solutions graphically.

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

• To graph the equations and find their intersection

• To eliminate one variable by adding or subtracting equations

• To substitute one equation into another

• To find the slope of the equations

In Example 1, what happens when you add two equations with opposite coefficients for one variable?

• The variable is eliminated

• The variable is halved

• The variable remains unchanged

• The variable is doubled

What is the result when two equations are added and their coefficients for a variable are opposites?

• The variable is eliminated

• The variable is doubled

• The variable is halved

• The variable remains unchanged

What is the outcome when two equations with opposite coefficients are added?

• The variable remains unchanged

• The variable is halved

• The variable is doubled

• The variable is eliminated

Why is it necessary to adjust equations in Example 2 before using elimination?

• To change the variables

• To simplify the equations

• To create opposite coefficients for one variable

• To make the equations identical

In Example 2, what is the result of multiplying the top equation by 2?

• The coefficients become opposites

• The coefficients become identical

• The equation is simplified

• The variables are changed

In Example 3, why are both equations multiplied by different numbers?

• To make the equations identical

• To change the variables

• To find a common multiple for elimination

• To simplify the equations

What is the significance of finding a common multiple in Example 3?

• To find a common solution

• To simplify the equations

• To eliminate a variable by subtraction

• To make the equations identical

What is the purpose of graphing the solutions in the final exercise?

• To substitute one equation into another

• To eliminate one variable

• To find the slope of the equations

• To verify the solutions by checking where the lines intersect

How does graphing help in verifying the solution of a linear system?

• It shows the slope of the equations

• It confirms the solution by showing the intersection point

• It eliminates one variable

• It substitutes one equation into another