If the equations 28x + 16y + 10 = 0 and 42x - ky - 14 = 0 have no solution, then the value of k is:

Two linear equations will have no solution if and only if the lines represented by them are parallel. Two lines are parallel if their slopes are equal.

The slope-intercept form of a linear equation is y = mx + c, where m is the slope.

Let's convert the given equations into slope-intercept form:

1. 28x + 16y + 10 = 0 can be rewritten as y = -(28/16)x - 10/16 = -7/4x - 5/8

So, the slope (m1) of the first line is -7/4.

2. 42x - ky - 14 = 0 can be rewritten as y = (42/k)x + 14/k

So, the slope (m2) of the second line is 42/k.

For the lines to be parallel, m1 must be equal to m2. Therefore, we set the two slopes equal to each other and solve for k:

-7/4 = 42/k

Cross-multiplying gives -7k = 168

So, k = 168 / -7 = -24

Therefore, the value of k for which the two equations have no solution is -24.