Question 656167
Solution for a system of linear equations is a common point in both equations 
that is the point where they intersect.

Two lines always intersect  unless they are parallel lines.
So if they are parallel lines there is no solution 

parallel lines have same slope

y = mx + c1 ------slope m

y = mx + c2 ------slope m


Represent the given equations in the slope intercept form

Equation 1
2x-y = 3
y = 2x-3 slope = 2

Equation 2 
4x+ky = 5
ky = -4x + 5 
y = -4x/k + 5/k

for the slope to be the same as equation 1  that is 2

-4/k = 2 

k = -2 

so if k = -2 both equations have same slope and they are parallel


if k = -2 there is no solution