Determine the Type of Solution | 8.EE.C.8

The video tutorial explores different types of solutions in systems of equations: no solution, one solution, and infinitely many solutions. It presents a specific system of equations and guides viewers through the process of determining the type of solution by solving the system. The tutorial explains that no solution occurs when the equations result in a false statement, one solution occurs when the equations intersect at a single point, and infinitely many solutions occur when the equations coincide. The video concludes by solving the example system, demonstrating that it has no solution.

What are the possible types of solutions for a system of equations?

• No solution, two solutions, infinitely many solutions

• No solution, one solution, two solutions

• One solution, two solutions, infinitely many solutions

• No solution, one solution, infinitely many solutions

What does it mean if a system of equations has no solution?

• The lines intersect at one point

• The lines intersect at two points

• The lines are parallel and never intersect

• The lines coincide completely

Why can a system of equations never have exactly two solutions?

• Because lines can only be perpendicular

• Because lines can only be parallel

• Because lines can only intersect at one point or coincide

• Because lines can only intersect at three points

What indicates that a system of equations has infinitely many solutions?

• The lines intersect at two points

• The lines coincide completely

• The lines intersect at one point

• The lines are parallel

What conclusion can be drawn if solving a system results in a false numerical statement?

• The system has infinitely many solutions

• The system has no solution

• The system has one solution

• The system has two solutions