Solving Systems by Elimination Techniques

The video tutorial explains how to solve systems of equations using the elimination method. It begins with an introduction to the concept of elimination, where one variable is eliminated by adding equations. The tutorial provides four examples, each demonstrating the step-by-step process of solving for different variables, including X, Y, C, D, M, and N. The video emphasizes the importance of checking solutions and understanding the intersection of lines in a system.

What is the main goal of the elimination method in solving systems of equations?

• To eliminate one of the variables

• To find the slope of the lines

• To substitute one equation into another

• To graph the equations

In the first example, what is the value of x after elimination?

• 3

• 2

• 4

• 1

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

• Multiply the equations

• Substitute x back into one of the original equations

• Graph the equations

• Check the solution

In the second example, why do we multiply one of the equations by -1?

• To find the value of y

• To change the coefficients of both variables

• To eliminate the variable with the same coefficient

• To make the equations easier to solve

What is the value of D in the second example after elimination?

• 3

• -3

• -1

• 1

In the third example, what is the first step to eliminate a variable?

• Divide both equations by the same number

• Subtract one equation from the other

• Multiply one equation by a negative number

• Add the equations directly

What is the value of M in the third example after elimination?

• 5

• 6

• 7

• 8

In the final example, which variable is immediately eliminated?

• Z

• W

• Y

• X

What is the value of x in the final example after elimination?

• 4

• 5

• 2

• 3

What is the final solution (x, y) in the last example?

• (4, 6)

• (3, 5)

• (2, -2)

• (1, -3)