Given and

Let us consider the first inequality.

⇒ 7x – 1 < –6

⇒ 7x – 1 + 1 < –6 + 1

⇒ 7x < –5

(1)

Now, let us consider the second inequality.

⇒ 3x + 63 < 0

⇒ 3x + 63 – 63 < 0 – 63

⇒ 3x < –63

⇒ x < –21

∴ x ∈ (–∞, –21) (2)

From (1) and (2), we get

∴ x ∈ (–∞, –21)

Thus, the solution of the given system of inequations is (–∞, –21).