Solving Systems of Equations using Linear Combination

This video tutorial teaches how to solve systems of equations using linear combination, also known as elimination. It begins with an introduction to the method, followed by a review of verifying solutions. The tutorial then explores the effects of adding equations in a system and demonstrates graphing lines to estimate solutions. Finally, it provides a detailed walkthrough of solving a system using linear combination, emphasizing the importance of verifying solutions through both algebraic and graphical methods.

What is the method called that involves combining equations to eliminate a variable?

• Substitution

• Graphing

• Linear Combination

• Factoring

When checking if a point satisfies a system of equations, what must be true?

• The point must be on the x-axis

• The point must satisfy at least one equation

• The point must satisfy both equations

• The point must be on the y-axis

What happens to the solution of a system when you add the two equations together?

• The solution becomes zero

• The solution changes

• The solution becomes undefined

• The solution remains the same

In the example where X + Y = 5 and X - Y = 1, what is the solution after adding the equations?

• (2, 3)

• (5, 1)

• (1, 5)

• (3, 2)

What is the solution to the system -2X + 5Y = 1 and 2X + 4Y = -10 after using linear combination?

• (3, 1)

• (1, -3)

• (-1, 3)

• (-3, -1)