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

Answer:

$k=-\frac{2}{7}$

Step-by-step 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:

$\frac{a}{d}=\frac{b}{e}\neq\frac{c}{f}$

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

$\frac{2}{4}=\frac{-3k}{k+2}\\k+2=-6k\\k=-\frac{2}{7}$

But also:

$\frac{-3k}{k+2}\neq\frac{1}{5}$

Hence the value of k is -2/7.