Solution:

Understanding the Problem:
We are given two equations kx-2y=3 and 3x y=5. We need to find the value of k such that the two equations represent two intersecting lines at a unique point.

Method:
We can find the value of k by solving the two equations simultaneously and checking whether the lines intersect at a unique point. If the lines intersect at a unique point, then the value of k is the solution of the problem.

Solving the Equations:
Let's solve the given equations to find the value of k.

kx-2y=3
3x y=5

Multiplying the second equation by 2, we get:

6xy=10

Now, we can substitute y from the second equation in the first equation and get:

kx-2(5/3x)=3

Simplifying the equation, we get:

kx-10/3x=3

Multiplying the equation by 3, we get:

3kx-10x=9

Bringing all the terms to one side, we get:

3kx-10x-9=0

This is a quadratic equation in x. We can solve this equation using the quadratic formula.

The quadratic formula is:

x = [-b ± sqrt(b^2 - 4ac)]/2a

In our equation, a = 3k, b = -10, and c = -9. Substituting the values in the formula, we get:

x = [10 ± sqrt(100 + 108k)]/6k

Since the lines intersect at a unique point, the quadratic equation has only one root. This means that the discriminant of the quadratic equation is zero.

The discriminant is:

b^2 - 4ac = 100 + 108k

Setting the discriminant to zero, we get:

100 + 108k = 0

Solving for k, we get:

k = -25/27

Conclusion:
Therefore, the value of k is -25/27.

K=-6

As the points are intersecting so a1/a2=b1/b2
Therefore, k/3=-2/1
So, our answer is -6