Question

Find the Values of k for which the following simultaneous equations have no solutions:

2x - 3ky = 1
4x + (k + 2)y = 5​

Answer 1

`k=-(2)/(7)`

Explanation:

The two equations given represent two straight lines in 2-D graph.

The two lines will not intersect if they are parallel.

Hence the two equations will not have solution if the lines are parallel and not coincident.

The condition for 2 lines given by the equations :

ax+by+c=0

dx+ey+f=0 to be parallel but not coincident is:

`(a)/(d)=(b)/(e)\\eq(c)/(f)`

here a=2 b=-3k c=-1 d=4 e=k+2 f=-5

`(2)/(4)=(-3k)/(k+2)\\k+2=-6k\\k=-(2)/(7)`

But also:

`(-3k)/(k+2)\\eq(1)/(5)`

Hence the value of k is -2/7.