Which statement about this system of equations is true?

To determine the nature of the system of equations represented by the two declining diagonal curves, we need to consider the points they pass through and how they relate to each other.

1. The first curve passes through the points:
- (-7, 4.9)
- (-5, 3)
- (0, 0)
- (3, -2)
- (6, -4)

2. The second curve passes through the points:
- (-7, 7.5)
- (-3, 5)
- (0, 3)
- (3, 1)
- (7, -2)

From the points listed, we can see that:

- The first curve intersects the second curve at (3, -2), because both curves pass through this point.
- They also do not share any other common points from the given points.

Now let's analyze the answer choices:

A. The system has no solution.
**Not true; they intersect at (3, -2).**

B. The system has a unique solution at (0,0).
**This is not correct; (0,0) lies on the first curve but not on the second.**

C. The system has a unique solution at (0,3).
**Not true; (0,3) lies on the second curve but not on the first.**

D. The system has infinitely many solutions.
**Not true; since the curves intersect at only one point, there are not infinitely many solutions.**

Only option A appears viable at first glance, but since both curves intersect at exactly one point, we realize that the correct choice should reflect that they indeed have a single unique solution at (3, -2). However, this specific point was not mentioned in the answer choices presented.

Given the options available and the nature of the solution, **none of the provided statements is correct.** If we must select from the only choices, the closest is that they intersect implying not "no solutions" as stated in A, **but rather there's a unique solution, which goes unrecognized in the options.**

Therefore, if forced to answer, given there's no option for the actual solution (3, -2) but recognizing that they do intersect, we might lean toward **Option as it least implies acknowledgment of a solution conflict, albeit incorrectly stated.