One of the most important and conceptual question from linear equations in two variables in which we have given two equations x+2y=5, 3x+ky+15=0 and we have to find the value of k for which it has a unique solution and also asked to solve for which it has no solution

Kindly solve the above equations

RS Aggarwal, Class 10, chapter 3D, question no 13

(i)

## x+2y=5,3x+ky+15=0

Here,

a1â€‹=1, b1â€‹=2, c1â€‹=âˆ’5

a2â€‹=3, b2â€‹=k, c2â€‹=15

a1/a2=1/2â€‹, b1/b2â€‹â€‹=2/k, c1/c2=âˆ’5â€‹/15=âˆ’1/3â€‹

a unique solution

a1/a2â‰ b1/b2â€‹â€‹â‡’1/2â‰ 2/kâ€‹

kâ‰ 4

(ii) a1/a2â‰ b1/b2â‰ c1/c2

Â Â Â 1/2=2/kâ‰ -1/3

Â Â Â k=4