Explanation

Let's denote the two numbers as x and y, where x is the smaller number.

Given:

x + y = 16 ... (1)

xy = 63 ... (2)

From (1), y = 16 - x. Substituting into (2):

x(16 - x) = 63

16x - x² = 63

x² - 16x + 63 = 0

Factoring the quadratic equation:

(x - 7)(x - 9) = 0

x = 7 or x = 9

Since x is the smaller number, x = 7.