We have,

x + 2y – 3 = 0

And, 5x + ky + 7 = 0

Here, a₁ = 1, b₁ = 2 and c₁ = – 3

a₂ = 5, b₂ = k and c₂ = 7

∴

And,

We know that, for the system having no solution we must have:

∴ k = 10

Hence, option A is correct