which of the following pairs of equations has exactly the same solution

Answer 1

To determine which pair of equations has exactly the same solution, we need to compare their slopes and y-intercepts.

1) y = 2x + 3
2) y = 2x - 1

The slopes for both equations are the same, which is 2. This means that both equations represent lines with the same steepness. However, the y-intercepts are different (3 for equation 1 and -1 for equation 2), which means that the lines will intersect at different points. Therefore, this pair of equations does not have exactly the same solution.

3) y = 4x + 1
4) y = 4x + 1

Both equations have the same slope (4) and the same y-intercept (1), so they represent the same line. Since they are equivalent, they have exactly the same solution.

Therefore, the correct answer is the pair of equations (3) and (4): y = 4x + 1.