Solving Linear Systems with Substitution Techniques

What are the three possible outcomes when solving systems of linear equations?

• One solution, no solution, infinitely many solutions

• One solution, two solutions, infinitely many solutions

• No solution, two solutions, infinitely many solutions

• One solution, no solution, three solutions

If two lines intersect at one point, what does this imply about the system of equations?

• There is no solution

• There is exactly one solution

• There are infinitely many solutions

• The lines are parallel

In the example where 2x + 4y = 4 and y = x - 2, what is the value of x?

• 0

• 1

• 3

• 2

What does the statement '8 equals 0' imply about the system of equations?

• The system has no solution

• The system has one solution

• The system has infinitely many solutions

• The system is inconsistent

In the example where x + 3y = 6 and 2x + 6y = -12, what does the result '12 = -12' indicate?

• The system is dependent

• The system has infinitely many solutions

• The system has no solution

• The system has one solution

What does the statement '0 equals 0' imply about the system of equations?

• The system has no solution

• The system has one solution

• The system has infinitely many solutions

• The system is inconsistent

In the example where 2x - 3y = 6 and 4x - 6y = 12, what does the result '12 = 12' indicate?

• The system has infinitely many solutions

• The system is inconsistent

• The system has no solution

• The system has one solution

What happens if one line is a multiple of the other in a system of linear equations?

• The lines are parallel

• The lines intersect at one point

• The lines are the same

• The system has no solution

What is the main idea behind the substitution method for solving systems of linear equations?

• Graph the equations and find the intersection point

• Solve for one variable and substitute it into the other equation

• Eliminate one variable by addition

• Write the equations in matrix form

Which of the following is NOT a method mentioned for solving systems of linear equations?

• Substitution

• Elimination by addition

• Matrix form

• Graphical method