Final answer:
The system of equations cannot be analyzed to determine the number of solutions due to the presence of a cubic term in the second equation.
Step-by-step explanation:
The given system of equations is:
y = -x + 7
y = -2r^3 + 512 + 1
To determine the number of solutions, we need to examine if the two equations represent parallel lines, intersecting lines, or the same line. If the slopes of the lines are equal and the y-intercepts are different, then the lines are parallel and there is no solution. If the slopes and y-intercepts are different, the lines will intersect at one point, indicating one solution. If the slopes are equal and the y-intercepts are equal as well, the lines will coincide and have infinite solutions.
However, in this particular case, the second equation involves a cubic term and does not have the same form as a linear equation. Therefore, we cannot directly determine the number of solutions. Without additional information or the ability to simplify the second equation, we cannot confidently state the number of solutions.