For which values of k does have no solution "kx + y = 1" "x + ky = 1"

When they are paralell

hum

kx+y=1
x+ky=1

if k=0 then they intersect at (1,1)
if k=1, they are the same equation
they have to be paralell, so  same slope

solve for y to get y=mx+b

y=-kx+1 and
y=-x/k+1/k

the slopes are -k and -1/k
slopes must be the same
-k=-1/k
times -1 both sides
k=1/k
times k both sides
k^2=1
k=1 or -1

1 doesn't work so k=-1

answer is k=-1