Question

For what value of k will the system of linear equation has unique solution and no solution x+2y = 5 , 3x+ky =15

Answer 1

a1=1 b1=2 c1=5

a2=3 b2=k c2=15

⭐If it have unique solution
then, a1/a2≠b1/b2

1/3≠2/k

k≠6

The value of k can be any no. except 6

⭐If it have no solution
then, a1/a2=b1/b2≠c1/c2

firstly taking,

a1/a2=b1/b2

1/3=2/k

k=6

secondly taking,

b1/b2≠c1/c2

2/k≠5/15

2/k≠1/3

k≠6