Find the value of k for which each of the following systems of equations has no solution:

Question

Find the value of k for which each of the following systems of equations has no solution: 8x + 5y = 9, kx + 10y = 15.

Philoid · Accepted Answer

Given: 8x + 5y = 9 – eq 1

kx + 10y = 15 – eq 2

Here,

a₁ = 8, b₁ = 5, c₁ = - 9

a₂ = k, b₂ = 10, c₂ = - 15

Here,

Given that system of equations has no solution

∴ = ≠

= ≠

Here,

=

8×10 = 5×k

5k = 80

K =

k = 16

∴ k = 16