Final answer:
If the two equations have no solution, the value of k is 3.
Step-by-step explanation:
If the two equations 2x+ky=5 and 6x+9y=10 have no solution, it means that these two equations represent parallel lines that will never intersect. In order to find the value of k, we need to compare the slopes of these lines. The slopes of the lines represented by the equations 2x+ky=5 and 6x+9y=10 are respectively -2/k and -2/3. If the two lines are parallel, the slopes should be equal, which means that -2/k = -2/3. By cross-multiplication, we can solve for k:
-2/k = -2/3
-2 * 3 = -2 * k
-6 = -2k
k = -6 / -2 = 3
So, if the two equations have no solution, the value of k is 3.