Understanding Solutions to Systems of Linear Equations

The video tutorial explores how to determine the number of solutions in a system of linear equations using both graphical and algebraic methods. It covers scenarios with no solutions (parallel lines), infinite solutions (identical lines), and one solution (unique intersection). The tutorial provides step-by-step algebraic solutions and explains the graphical interpretation of each case.

What are the possible outcomes when solving a system of linear equations graphically?

• Only no solutions

• Only infinitely many solutions

• Only one solution

• No solutions, one solution, or infinitely many solutions

What does it mean if a system of equations results in a statement like 0 = -20?

• The system has infinitely many solutions

• The system is inconsistent

• The system has no solutions

• The system has one solution

If two lines are parallel, what can be said about the system of equations?

• The system has one solution

• The system has no solutions

• The system has infinitely many solutions

• The system is consistent

If two equations in a system are equivalent, what does this imply about their solutions?

• There is no solution

• The system is inconsistent

• There is exactly one solution

• There are infinitely many solutions

What is the result when two lines in a system of equations coincide?

• No solution

• Infinitely many solutions

• One solution

• Inconsistent system

What does a statement like -5 = 20 indicate about a system of equations?

• The system has one solution

• The system has no solutions

• The system has infinitely many solutions

• The system is consistent

What is the solution to the system if you derive 5y = -5?

• y = 0

• y = 5

• y = 1

• y = -1

What does it mean if a system of equations results in 0 = 0?

• The system is inconsistent

• The system has infinitely many solutions

• The system has one solution

• The system has no solutions

What does it mean if a system of equations has a unique solution?

• The lines are parallel

• The lines intersect at one point

• The lines coincide

• The system is inconsistent

What can be concluded if a system of equations results in a true statement like 0 = 0?

• The system has no solutions

• The system has one solution

• The system has infinitely many solutions

• The system is inconsistent