Systems - Consistent, Inconsistent, Dependent or Independent

When solving a system of linear equations, what does an algebraic outcome of "0 = 9 False" signify?

• One unique solution

• Infinitely many solutions

• No solution

What graphical representation corresponds to a system of linear equations with infinitely many solutions?

• Intersecting lines

• Parallel lines

• The same line

How is a system of linear equations classified if it has at least one solution?

• Inconsistent

• Dependent

• Consistent

A system of linear equations is classified as dependent under which condition?

• The equations represent the same line

• The equations represent parallel lines with different y-intercepts

• The equations intersect at a single point

When solving a system of linear equations algebraically, if the process results in a true statement like -20 = -20, what does this indicate about the system?

• One unique solution

• Infinitely many solutions

• No solution

If solving a system of linear equations algebraically leads to a false statement, such as -2 = 6, what is the nature of the solution set for this system?

• One unique solution

• Infinitely many solutions

• No solution

A system of two linear equations has slopes of 3 and -2/5, and y-intercepts of -7 and 6, respectively. How many solutions does this system have?

• One solution

• Infinitely many solutions

• No solution

Consider a system of two linear equations where both equations have the same slope but different y-intercepts. What can be concluded about the number of solutions and the classification of this system?

• One solution, consistent and independent

• Infinitely many solutions, consistent and dependent

• No solution, inconsistent and independent