Multiple Choice Question

The graph below represents a system of equations.

A line passing through (-2, 0) and (0, -3), another line passing through (0, 1) and (2, 0) intersect at (-4, 3).

Which of the following statements is true?

A.
The system has infinite solutions.

B.
The solutions to the system are
and
.

C.
The solution to the system is
.

D.
The system has no solution.

1 answer

To analyze the scenario based on the description provided about the lines in the graph, let’s break down the statements:

  1. Identifying the lines and intersection:
    • The first line passes through points (-2, 0) and (0, -3).
    • The second line passes through points (0, 1) and (2, 0).

Given the description, the lines intersect at a single point (-4, 3).

  1. Evaluating the statements:
    • A. The system has infinite solutions.

      • This is false, as the lines intersect at a single point.
    • B. The solutions to the system are and.

      • This statement is incomplete and hence does not provide complete information.
    • C. The solution to the system is .

      • This statement is also incomplete without specifying what the solution is (likely meant to say (-4, 3), based on the intersection point).
    • D. The system has no solution.

      • This is false, as the lines do intersect.

Given that the lines intersect at a single point (-4, 3), the most accurate option, even though it's incomplete, would point to C as the correct choice for stating the solution if it were complete.

Assuming it were to say "The solution to the system is (-4, 3)", that would be true based on the description. Since the other options (A and D) are false and B is incomplete, C stands as the most relevant answer here, although it should ideally state the actual solution.

For a final selection: C (assuming it completes to point to the solution).