Let's analyze the pair of equations [tex]\( y = 0 \)[/tex] and [tex]\( y = -7 \)[/tex].
1. Understanding the Equations:
- The equation [tex]\( y = 0 \)[/tex] represents a horizontal line that intersects the y-axis at 0 (the x-axis itself).
- The equation [tex]\( y = -7 \)[/tex] represents a horizontal line that intersects the y-axis at -7.
2. Graphical Representation:
- On a Cartesian plane, [tex]\( y = 0 \)[/tex] is a horizontal line passing through the origin.
- [tex]\( y = -7 \)[/tex] is another horizontal line parallel to [tex]\( y = 0 \)[/tex] but located 7 units below the x-axis.
3. Checking for Intersection:
- Since both lines are horizontal and parallel, they will never intersect.
- Parallel lines have no common points.
4. Conclusion:
- Because the lines [tex]\( y = 0 \)[/tex] and [tex]\( y = -7 \)[/tex] do not intersect, there are no points that satisfy both equations simultaneously.
- Therefore, the pair of equations has no solutions.
Given the analysis above, the correct answer is:
(d) no solution
