4x+ky=6 and kx+y=-3

Question

Find the values of the constant k such that the system of the linear equation

Answer 1

ky = -4x + 6

 

y = (-4/k)x + (6/4)

 

  = (-4/k)x + 3/2

 

vs.

 

y = -kx + -3

 

For the system to have a unique solution, the slopes must be different.

 

If -k = -4/k, the slopes will be the same and the lines will be parallel,

so there will be no solution.

For this to happen,  k = 4/k

                             k^2 - 4 = 0

                             k = +or- 2