The pair of equation y = 0 and y = 5 has solutions :

Question

Accepted Answer

The pair of equations given are y = 0 and y = 5. Let's analyze these equations to determine the number of solutions they have.

1. **Explanation for Option 3 (No Solution):**
   - The equation y = 0 represents a horizontal line on the Cartesian plane where the y-coordinate of every point on the line is 0.
   - Similarly, the equation y = 5 represents another horizontal line where the y-coordinate of every point on this line is 5.
   - For a pair of equations to have a solution, there must be at least one point that satisfies both equations simultaneously.
   - In this case, there is no point that can have a y-coordinate of both 0 and 5 at the same time. Therefore, these two lines are parallel and do not intersect at any point.
   - Since there is no intersection point, the pair of equations has no solution.

2. **Explanation for why other options are incorrect:**
   - **Option 1 (One Solution):** This option is incorrect because for there to be one solution, the two lines would need to intersect at exactly one point. However, as explained, the lines y = 0 and y = 5 are parallel and do not intersect at any point.
   - **Option 2 (Two Solutions):** This option is incorrect because two linear equations can intersect at most at one point in a two-dimensional plane. Since these lines are parallel, they do not intersect at all, let alone at two points.
   - **Option 4 (Infinitely Many Solutions):** This option is incorrect because infinitely many solutions would imply that the two equations represent the same line, meaning they would overlap completely. However, y = 0 and y = 5 are distinct parallel lines and do not overlap.

In conclusion, the correct answer is Option 3: no solution, because the lines represented by the equations y = 0 and y = 5 are parallel and do not intersect at any point.