Find k for which the system x + 2y = 3 and 5x + ky + 7 = 0 is inconsistent.

The given two equations are:

x + 2y – 3 = 0 …(i)

5x + ky + 7 = 0 …(ii)

Here, we have:

a₁ = 1, b₁ = 2 and c₁ = – 3

a₂ = 5, b₂ = k and c₂ = 7

We know that, for the system to be consistent we must have

k = 10

Hence, the value of k is 10