Find a value for a that will give the following system no solution.

4ax+5y=10
2x-3y=9

The question I am asking is how do I arrive at the answer? Just posting the answer will not help me...The slope needs to be the same and the y-intercepts need to be different, but I'm having trouble arriving at the answer. Any help would be great and I will choose best answer for the most helpful answer!

4ax+5y=10
5y = -4ax +10
y = -4a/5 x +2 (1)

2x-3y=9
3y = 2x -9
y = 2/3 x -3 (2)

You are correct in the way to solve this question.
"The slope needs to be the same and the y-intercepts need to be different"
ie They need to be distinct parallel lines.
The slope are identical when
-4a/5 = 2/3
a = -5/4 *2/3 = -10/12 = - 5/6
When a = -5/6 both equations will have the slope = 2/3
Equation (1) has a y-intercept of 2 and equation (2) has a y-intercept of -3
Because they distinct parallel lines , they will never intersect and therefore will have no points
in common.

Put both into slope-intercept form:

2x-3y=9
2x-9=3y
y=(2/3)x-3

4ax+5y=10
5y=-4ax+10
y=(-4/5)ax+2

So the y-intercepts are already different, and to make the slopes the same, (-4/5)a must equal 2/3.
(-4/5)a = 2/3
-12a = 10
a = -5/6