How to solve a system of equations by elimination | 8 examples

The video tutorial by Brian Mclogan covers solving systems of equations using the elimination method. It includes eight examples demonstrating different scenarios: no multipliers, one multiplier, two multipliers, infinite solutions, and no solutions. The tutorial emphasizes the importance of eliminating one variable at a time and using addition or subtraction to simplify equations. It also highlights the use of multipliers to align coefficients and solve more complex systems. The video concludes with a summary of the key points and encourages viewers to practice the techniques discussed.

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

• To substitute one equation into another

• To find the slope of each equation

• To graph the equations and find the intersection point

• To eliminate one variable by combining equations

When combining equations in the elimination method, what is a common strategy to simplify the process?

• Graph the equations first

• Use division to simplify coefficients

• Convert subtraction problems into addition

• Always use subtraction

In the elimination method, what happens when you end up with a statement like 0 = 0?

• The equations are inconsistent

• There are infinite solutions

• The solution is a single point

• There is no solution

What does it mean if, after elimination, you get a false statement like 0 = -18?

• The system is dependent

• The system has a unique solution

• The system has infinite solutions

• The system has no solution

How do you decide which variable to eliminate first in a system of equations?

• Choose the variable with the smallest coefficient

• Choose the variable that appears in both equations

• Choose the variable that is not present in one equation

• Choose the variable that makes the math easier

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

• To find the intersection point of the graphs

• To make the coefficients of a variable the same

• To simplify the equations

• To determine the slope of the lines

When using two multipliers in the elimination method, what is the goal?

• To make both equations identical

• To eliminate both variables simultaneously

• To find the solution without graphing

• To make the coefficients of one variable equal and opposite

What should you do if the coefficients of the variables are not the same in both equations?

• Graph the equations instead

• Switch to the substitution method

• Ignore the coefficients and solve directly

• Use a multiplier to adjust the coefficients

How can you verify the solution of a system of equations solved by elimination?

• By checking if the solution satisfies only one equation

• By substituting the solution back into the original equations

• By solving the system using substitution

• By graphing the equations and checking the intersection

What is a potential outcome when solving a system of equations with elimination?

• A single solution point

• No solution

• Infinite solutions

• All of the above