To analyze the system of equations given:
- \( y = -3x + 7 \)
- \( y = -3x - 7 \)
Both equations have the same slope of \(-3\) but different y-intercepts (7 and -7).
This means that the lines represented by these equations are parallel. Since parallel lines never intersect, the system has no solutions.
Therefore, the correct statement is:
Both equations have a slope of -3, but they do not share the same y-intercept. Thus, the system has no solutions because the lines are parallel.