Elimination Method in Solving Systems of Equations

The video tutorial explains solving systems of equations using the elimination method. It begins by discussing why substitution might not be ideal when no variable has a coefficient of one. The teacher then introduces elimination, explaining how to add or subtract equations to eliminate a variable. The process involves finding common multiples and adjusting equations accordingly. The tutorial walks through solving for x and y, emphasizing the importance of making one coefficient negative to eliminate a variable. The session concludes with a complete solution and an example, reinforcing the method's application.

Why is substitution not ideal in this problem?

• Because it involves solving for a variable with a coefficient of one.

• Because it leads to complex fractions.

• Because it requires graphing the equations.

• Because it is not a valid method for this type of problem.

What is the main goal of the elimination method?

• To find the common multiple of the coefficients.

• To graph the equations.

• To eliminate one of the variables by adding or subtracting the equations.

• To solve for one variable directly.

What is the first step in the elimination method?

• Solve for one variable.

• Find the common multiple of the coefficients.

• Graph the equations.

• Check if the equations are consistent.

What is the common multiple of 4 and 3?

• 15

• 6

• 9

• 12

Why is it necessary to make one of the coefficients negative when adding the equations?

• To ensure the equations are consistent.

• To eliminate the variable by making the sum zero.

• To simplify the equations.

• To avoid fractions.

What is the result of adding 9x + 12y = 30 and -8x - 12y = -28?

• x = 0

• x = -2

• x = 2

• x = 1

After finding x, what is the next step?

• Substitute x back into one of the original equations.

• Graph the equations.

• Check for consistency.

• Solve for another variable.

Which equation is used to find y after determining x?

• 3x + 4y = 10

• 4x + 3y = 12

• -8x - 12y = -28

• 9x + 12y = 30

What is the value of y when x = 2?

• y = -1

• y = 0

• y = 1

• y = 2

What is the final solution to the system of equations?

• (2, 0)

• (1, 2)

• (2, 1)

• (1, 1)