Given the quadratic equations I. a² - 13a + 42 = 0 and II. b² - 15b + 56 = 0, determine the correct relationship between the values of a and b obtained by solving these equations.

Explanation

Solving the first equation: a² - 13a + 42 = 0 factors as (a - 6)(a - 7) = 0, giving a = 6 or 7. Solving the second equation: b² - 15b + 56 = 0 factors as (b - 7)(b - 8) = 0, giving b = 7 or 8. Comparing the values, the maximum value of a is 7 and the minimum value of b is 7, so a is always less than or equal to b.