Elimination Method in Systems of Equations

This video tutorial focuses on solving systems of equations using the elimination method, also known as the addition method. It covers examples of solving systems with two and three variables, including systems with fractions. The video provides step-by-step instructions on how to eliminate variables to find solutions, and it emphasizes checking solutions for accuracy.

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

• To find the determinant of the matrix

• To eliminate one variable by adding or subtracting equations

• To convert the system into a single equation

• To graph the equations and find the intersection

In the example 2x - y = 3 and 3x + y = 7, what is the value of x after eliminating y?

• 2

• 1

• 3

• 4

When solving a system with fractions, what is the first step to simplify the process?

• Convert the fractions to decimals

• Subtract the equations

• Multiply each term by the least common multiple of the denominators

• Add the equations directly

What is the least common multiple of 3 and 2, used to clear fractions in the equation 1/3x - 1/2y = -2?

• 3

• 6

• 4

• 5

In a system with three variables, why might it be easier to eliminate the variable y first?

• Y often has coefficients that are easier to manipulate

• Y is the most common variable

• Y is the first variable in the alphabet

• Y always has the smallest coefficient

When solving the system x + y + z = 6, 2x + y - z = 1, and 3x - y + 2z = 7, what is the first step?

• Solve for x in the first equation

• Eliminate x from all equations

• Eliminate z from all equations

• Eliminate y from two equations

In the system 2x - y + 3z = 15, 3x + 2y - 4z = 11, and 4x - 3y + 2z = 14, what is the value of z after elimination?

• 2

• 1

• 3

• 4

What is the common multiple used to eliminate x in the system of equations with three variables?

• 7

• 14

• 21

• 28

After finding x = 5 and z = 3 in the three-variable system, what is the value of y?

• 5

• 3

• 2

• 4

What is the final solution for the system 2x - y + 3z = 15, 3x + 2y - 4z = 11, and 4x - 3y + 2z = 14?

• (5, 3, 4)

• (5, 4, 3)

• (4, 5, 3)

• (3, 4, 5)