m = 4 (option A)
Explanation:[tex]\begin{gathered} \text{Given: } \\ \text{y = 4x + 1 }\ldots(1) \\ y\text{ = mx - 5 }\ldots(1) \end{gathered}[/tex]For the system of equations to have no solution, it means they do not intersect. For this to happen, they would have same slope.
using equation of line:
y = mx + b
m = slope, b = y-intercept
Slope for the 1st equation:
m = 4
Slope for the 2nd equation will also be equal to 4
the 2nd equation becomes:
y = 4x - 5
This makes both equations to be parallel lines. Parallel lines donot have point of intersection (no solution).
Hence, the value of m that would make the system of equations have no solution is 4
