Solving Systems of Equations

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.