An important and conceptual question from linear equations in two variables in which we have given two equations kx+2y=5, 3x-4y=10 and we have been asked to find the value of k in such a way that it has a unique solution and also asked to solve these equations in such a way that it has no solution

RS Aggarwal, Class 10, chapter 3D, question no 12

(i) Here,

a1â€‹=k, b1â€‹=2, c1â€‹=5

a2â€‹=3, b2â€‹=âˆ’4, c2â€‹=10

a1/a2â€‹â€‹=k/3, b1/b2â€‹â€‹=2/-4â€‹=âˆ’1/2â€‹

c1/c1â€‹â€‹2=5â€‹/10=1/2â€‹

System has a unique solution.

a1/a2â‰ b1/b2â€‹â€‹â‡’k/3â‰ -1/2â€‹

kâ‰ âˆ’3/2

(ii) If system has a no solution.

a1/a2=b1/b2â€‹â€‹â‰ 1/2â€‹

k/3=âˆ’1â€‹/2â‰ 1/2â€‹

kâ‰ 3/2