Final answer:
The correct answers are C. consistent, dependent, dependent, consistent. A consistent system has at least one solution, while a dependent system has infinite solutions because it describes the same line graphed multiple times.
Step-by-step explanation:
The correct answer to the fill-in-the-blank question is: A consistent Response area system has at least one solution. A dependent Response area system has an infinite number of solutions. The system of equations graphed is consistent Response area and dependent Response area. Therefore, the correct combination of words to fill in the blanks is C. consistent, dependent, dependent, consistent.
In the context of systems of linear equations:
A consistent system has at least one solution, which means the lines intersect at least at one point or are the same line (coincident).
A dependent system has an infinite number of solutions because it represents the same line graphed twice, so every point on the line is a solution.
In a graph, the variables plotted on the axes represent a relationship between an independent variable (x-axis) and a dependent variable (y-axis). The dependent system is consistent because the equations describe the exact same line, and any solution to one equation in the system is also a solution to the other.