Question

for how many values of k does the the following system of equations have at least one solution?
x+y=1; kx+y=3; x+ky=5

Answer 1

x+ky=5
have atleast 1 solu

Answer 2

let x+y=1........(1)
kx+y=3..........(2)
x+ky=5..........(3)

adding 2 and 3 => (k+1)(x+y)=8
we want at least one solution. hence comparing with (1) we get k+1=8=>k=7.