Question

If the system of equations x + ky = 0, 2x - y = 0 has unique solution, write the condition?​

Answer 1

Step-by-step explanation:

for unique solution these lines must be intersect each other at only one point.

$x + ky = 0.......(1) \\ 2x = y.......(2)$

from equation 1 and 2 , we have

$x + 2kx = 0 \\ = > x(1 + 2k) = 0$

if x is not equal to zero. then

$(1 + 2k ) \: must \: be \: zero.$

$= > 1 + 2k = 0 \\ = > k = - 1 \div 2$

but if you check the value of k in any eq 1 or 2 you get only one straight line.

So for its unique solution,

k is never gonna be -1/2.