This video tutorial explains 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 to systems of equations. The tutorial then explores the effect of adding equations in a system and demonstrates how this maintains the solution. Finally, it provides a detailed example of solving a system both graphically and algebraically, emphasizing the importance of checking solutions through both methods.

What is another name for the linear combination method?

• Elimination

• Matrix Method

• Graphing

• Substitution

What must be true for a point to satisfy a system of equations?

• It must be a positive integer.

• It must make both equations true.

• It must make one equation true.

• It must be a negative integer.

If a point (3, 5) satisfies the system x + y = 8 and x - y = -2, what does this imply?

• The point satisfies neither equation.

• The point satisfies both equations.

• The point only satisfies the second equation.

• The point only satisfies the first equation.

What happens to the solution when two equations in a system are added together?

• The solution becomes undefined.

• The solution becomes zero.

• The solution remains the same.

• The solution changes.

What is the result of adding x + y = 5 and x - y = 1?

• x = 5

• x = 4

• x = 3

• x = 2

What is the estimated solution when graphing the system -2x + 5y = 1 and 2x + 4y = -10?

• (-3, 1)

• (1, -3)

• (-2, 0)

• (0, -1)

What is the value of y when solving the system -2x + 5y = 1 and 2x + 4y = -10 using linear combination?

• y = 2

• y = 0

• y = -1

• y = 1

After finding y = -1, what is the next step to find x in the system -2x + 5y = 1?

• Substitute y = -1 into the first equation.

• Substitute y = -1 into the second equation.

• Substitute y = -1 into both equations.

• Substitute y = -1 into neither equation.

What is the final solution for x in the system -2x + 5y = 1 and 2x + 4y = -10?

• x = -1

• x = -4

• x = -2

• x = -3

Why is it important to verify the solution by substituting back into the original equations?

• To check if the solution is a positive number.

• To ensure the solution satisfies both equations.

• To verify the solution is a fraction.

• To confirm the solution is a whole number.