Question
The graph below represents a system of equations.

Which of the following statements is true?
A.
The system has infinite solutions.
B.
The solutions to the system are (0,1) and (0,−3).
C.
The solution to the system is (−4,3).
D.
The system has no solution.

Which of the following statements is true?
A.
The system has infinite solutions.
B.
The solutions to the system are (0,1) and (0,−3).
C.
The solution to the system is (−4,3).
D.
The system has no solution.
Answers
GPT-4o mini
To determine which statement is true about the system of equations represented by the graph, we need to analyze the characteristics of the lines. Here’s a guide for evaluating each option:
A. **The system has infinite solutions.**
This is true if the two lines are coincident (i.e., they lie on top of each other). If the lines are parallel, then this statement is false.
B. **The solutions to the system are (0,1) and (0,−3).**
This would imply that both points are intersection points or solutions to the system. Check if both points are where the lines intersect or lie on either line.
C. **The solution to the system is (−4,3).**
This means that (−4,3) is the intersection point of the two lines. Check the graph for the coordinates and see if it meets at this point.
D. **The system has no solution.**
This is true if the two lines are parallel and do not intersect at any point.
Since I cannot see the graph, I suggest examining the lines according to the options given. The correct option will depend on whether the lines intersect at a single point, are parallel, or are coincident. If they intersect at one unique point, select Choice C; if they are parallel, choose D; if they overlap at many points, choose A; and if (0,1) or (0,−3) is on the lines, refer to B.
Please inspect the graph closely for clarity on these intersection properties.
A. **The system has infinite solutions.**
This is true if the two lines are coincident (i.e., they lie on top of each other). If the lines are parallel, then this statement is false.
B. **The solutions to the system are (0,1) and (0,−3).**
This would imply that both points are intersection points or solutions to the system. Check if both points are where the lines intersect or lie on either line.
C. **The solution to the system is (−4,3).**
This means that (−4,3) is the intersection point of the two lines. Check the graph for the coordinates and see if it meets at this point.
D. **The system has no solution.**
This is true if the two lines are parallel and do not intersect at any point.
Since I cannot see the graph, I suggest examining the lines according to the options given. The correct option will depend on whether the lines intersect at a single point, are parallel, or are coincident. If they intersect at one unique point, select Choice C; if they are parallel, choose D; if they overlap at many points, choose A; and if (0,1) or (0,−3) is on the lines, refer to B.
Please inspect the graph closely for clarity on these intersection properties.