Question

For which value of m would the system of equations y = 4x + 1 and y = mx – 5 have no solution?O A. m = 4O B. m = 1O c. m = -5O D. m = -4

Answer 1

m = 4 (option A)

Explanation:$\begin{gathered} \text{Given: } \\ \text{y = 4x + 1 }\ldots(1) \\ y\text{ = mx - 5 }\ldots(1) \end{gathered}$

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