Solving Systems of Equations Using Elimination

In this tutorial, the teacher explains how to solve systems of equations using the elimination method. The lesson focuses on a scenario where the variables do not initially align, requiring multiplication of one equation to match the variables. Once aligned, the equations are added to eliminate one variable, and the remaining variable is solved. The solution is verified by substituting back into the original equations.

What is the first step if the variables in two equations do not match?

• Add the equations directly

• Subtract one equation from the other

• Multiply one or both equations to match variables

• Divide one or both equations

What was the purpose of multiplying one of the equations by 3?

• To simplify the equation

• To find the value of X directly

• To make the coefficients of Y match

• To eliminate the X variable

Why do we multiply an equation before adding or subtracting in the elimination method?

• To simplify the equations

• To directly find the value of one variable

• To reduce the equations to a single variable form

• To make the coefficients of one variable match

What is the significance of the coefficients matching after multiplying an equation?

• It indicates the equations are identical

• It simplifies the equations further

• It allows for the direct solution of both variables

• It enables the elimination of one variable when added

After matching the variables, what is the next step in solving the system of equations?

• Multiply the equations

• Add the equations to eliminate a variable

• Graph the equations

• Substitute one equation into the other

What is the result of adding the two equations after matching the Y variables?

• Two separate equations for X and Y

• A new equation with both X and Y

• Elimination of the Y variable

• Elimination of the X variable

What happens to the Y variable after adding the modified equations?

• Its value is directly determined

• Its coefficient becomes zero, eliminating it

• It becomes the only variable in the equation

• It remains unchanged

How do you solve for Y after finding the value of X?

• Add X to one of the original equations

• Divide the equation by X

• Substitute X back into one of the original equations

• Multiply X by the coefficient of Y

What is the final solution for X and Y?

• X = 3, Y = 6

• X = 6, Y = 3

• X = 5, Y = 2

• X = 2, Y = 5

After finding X, which equation is used to find Y?

• The modified equation

• A new equation derived from the first two

• The original second equation

• Either of the original equations