Elimination Method in Systems of Equations

The video tutorial introduces the elimination method for solving systems of equations, explaining the process of aligning equations and making coefficients opposites to cancel variables. It provides step-by-step instructions and examples, demonstrating how to solve for one variable and substitute back to find the other. The tutorial includes multiple examples, from basic to advanced, and encourages students to practice and verify their solutions.

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

• To substitute one variable into another equation

• To graph the equations and find the intersection point

• To cancel out one of the variables by making coefficients opposites

• To solve each equation separately

Which of the following is NOT a method previously discussed for solving systems of equations?

• Graphing

• Substitution

• Elimination

• Integration

In the elimination method, what must be true for two coefficients to cancel each other out?

• They must be negative

• They must be positive

• They must be opposites

• They must be equal

What is the first step in solving a system of equations using the elimination method?

• Multiply the equations by a constant

• Graph the equations

• Solve for one variable

• Align the equations so that like terms are in columns

In the example provided, what was the result after adding the two equations together?

• 8x = 16

• x = 0

• x = 2

• y = -1

After finding the value of x in the example, what is the next step?

• Graph the solution

• Multiply the equations by a constant

• Solve for y using the original equations

• Check the solution by substituting back

What should you do if the coefficients are not initially opposites in the elimination method?

• Graph the equations instead

• Switch to the substitution method

• Multiply one or both equations by a constant to make them opposites

• Ignore the coefficients

In the additional examples, what was done to make the coefficients of y opposites?

• Added a constant to both equations

• Subtracted one equation from the other

• Divided the equations by a common factor

• Multiplied the entire equation by -1

What is a common strategy when dealing with challenging elimination problems?

• Multiply the equations to find a common multiple for coefficients

• Guess the solution and check

• Use a calculator to find the solution

• Switch to graphing the equations

In the challenging exercises, what was the solution for the system of equations in the final example?

• (5, -3)

• (8, 8)

• (2, 1)

• (6, 0)