Question

Find the value(s) of k for which the pair of equations
kx +  2y = 3
3x + 6y = 10 has a unique solution.

Answer 1

The given equations are
kx + 2y = 3
3x + 6y = 10
For a unique solution,
`a_1/a_2 ≠ b_1/b_2`
Where a₁= k, a₂ = 3, b₁ = 2, b₂ = 6.
`k/3 ≠ 2/6`
⇒ k ≠ 1
For all values of k except 1, the given linear equations will have a unique solution.