Solving Systems of Linear Equations Using the Linear Combination Method

This video tutorial teaches how to solve systems of linear equations using the linear combination method. It begins with an introduction to the method and a review of the multiplication property of equality. The tutorial then provides a detailed, step-by-step solution to two different systems of equations, demonstrating how to manipulate and combine equations to find the intersection point. The video emphasizes the importance of checking solutions by substituting them back into the original equations.

What is the main focus of this lesson?

• Graphing linear equations

• Solving a system of linear equations using the linear combination method

• Solving quadratic equations

• Understanding the properties of inequalities

What does the multiplication property of equality allow you to do?

• Add different numbers to both sides of an equation

• Subtract different numbers from both sides of an equation

• Multiply both sides of an equation by the same number

• Divide both sides of an equation by different numbers

In the first example, what is the result of combining the equations after adjusting the second equation?

• 10X = 19

• 5X = 10

• 8X = 16

• 12X = 24

What is a common mistake when writing the solution for a system of equations?

• Writing the solution in the form of first number found, second number found

• Writing the solution as a fraction

• Writing the solution in the form of Y, X

• Writing the solution as a single number

How do you verify the solution of a system of equations?

• By solving the equations again

• By graphing the equations and checking the intersection

• By checking if the point satisfies both equations

• By checking if the point satisfies only one equation

What is the first step in solving the second set of equations using the linear combination method?

• Divide the first equation by 2

• Subtract the first equation from the second

• Multiply the second equation by -1

• Add the equations directly

What is the solution for Y in the second example?

• Y = -22

• Y = 17

• Y = 22

• Y = -17

After finding Y, how do you solve for X in the second example?

• Substitute Y into the first equation

• Substitute Y into the second equation

• Subtract Y from the second equation

• Add Y to the first equation

What is the final solution for the second set of equations?

• (-17, 22)

• (-22, 17)

• (17, -22)

• (22, -17)

What is the significance of the point where the two equations intersect?

• It is the endpoint of the graph

• It is the starting point of the graph

• It is the solution to the system of equations

• It is the midpoint of the equations