Understanding the Elimination Method in Solving Linear Equations

The video tutorial explains how to solve a system of linear equations using the elimination method. It begins by introducing the concept of elimination, where equations are added to eliminate one variable. The tutorial then demonstrates how to prepare equations by making terms opposites, either by multiplying by constants or adjusting terms. The process of solving for X is shown by multiplying equations and simplifying. After finding X, the tutorial explains how to substitute it back into one of the original equations to solve for Y. Finally, the solution is verified by substituting the values back into both equations to ensure they satisfy the system.

What is the main goal when using the elimination method to solve a system of linear equations?

• To graph the equations and find the intersection

• To eliminate one variable by making its coefficients opposites

• To find the sum of the equations

• To multiply both equations by the same constant

In the elimination method, what must be true about the coefficients of the variable you want to eliminate?

• They must be opposites

• They must be zero

• They must be equal

• They must be positive

What operation is performed on the first equation to make the y terms opposites in this example?

• Add 5

• Multiply by 5

• Subtract 5

• Multiply by -5

After eliminating the y variable, what is the next step in solving the system of equations?

• Graph the equations

• Solve for y

• Check the solution

• Solve for x

What is the value of x after solving the equation -8x = 32?

• x = -4

• x = 4

• x = 8

• x = -8

Once x is found, what method is used to find the value of y?

• Graphing

• Substitution

• Elimination

• Trial and error

What is the ordered pair solution for the system of equations in this example?

• (4, 2)

• (4, -2)

• (-4, 2)

• (-4, -2)

Why is the system of equations considered consistent?

• It has no solution

• The equations are identical

• It has at least one solution

• The equations are dependent

What is the purpose of verifying the solution by substituting back into the original equations?

• To eliminate another variable

• To ensure the solution satisfies both equations

• To simplify the equations further

• To find a different solution

What is the result of substituting x = -4 and y = 2 into the first equation?

• -12 + 2 = -10

• -12 + 2 = 10

• 12 + 2 = 10

• 12 + 2 = -10