To solve this problem, we first solve 4x-3y-1=0 and 5x-2y-3=0 to find x and y for the intersection point.
To solve the system of equations, 4x - 3y = 1 and 5x - 2y = 3, we can use the substitution or elimination methods. Let's use the elimination method for this problem.
When we solve these equations, we get the point of intersection.
Next, we know that the equation of a line parallel to 2y-3x+2=0 can be expressed as -3x + 2y = k where k is a constant.
By substituting the x and y values from the intersection point we found earlier into this equation, we can solve for k.
With the value of k, the equation of the line would then be -3x + 2y - k = 0. This is the equation of the line that is parallel to 2y-3x+2=0 and that passes through the intersection of the first two lines.
Therefore, the answer is option C which states that the equation of the line is -3x + 2y - k = 0.