Systems of Equations Scenarios

The video tutorial explains systems of equations, focusing on scenarios with one solution, infinite solutions, or no solutions. It covers consistent and independent systems, dependent systems, and inconsistent systems. The tutorial provides examples to illustrate these concepts and guides viewers in analyzing systems to determine the number of solutions.

What are the three possible scenarios for systems of equations?

• One solution, infinite solutions, no solutions

• One solution, two solutions, infinite solutions

• Two solutions, infinite solutions, no solutions

• One solution, two solutions, no solutions

In the one solution scenario, what is true about the two lines?

• They are parallel

• They are the same line

• They do not intersect

• They intersect at one point

What does it mean when two lines are consistent and independent?

• They intersect at one point

• They do not intersect

• They have different slopes

• They are the same line

In the infinite solutions scenario, what is true about the two lines?

• They intersect at one point

• They do not intersect

• They are the same line

• They are parallel

What does it mean when two lines are consistent and dependent?

• They do not intersect

• They have different slopes

• They are the same line

• They intersect at one point

In the no solutions scenario, what is true about the two lines?

• They are parallel

• They are the same line

• They intersect at one point

• They have different slopes

What does it mean when two lines are inconsistent?

• They have different slopes

• They are the same line

• They do not intersect

• They intersect at one point

Given the system of equations 10x - 2y = 4 and 10x - 2y = 16, how many solutions exist?

• Two solutions

• One solution

• Infinite solutions

• No solutions

Given the system of equations -5x - y = 10 and 4x + y = 8, how many solutions exist?

• Two solutions

• Infinite solutions

• No solutions

• One solution

Given the system of equations 2x + y = -4 and y = -2x - 4, how many solutions exist?

• No solutions

• Two solutions

• Infinite solutions

• One solution