Given the equations I. x² - x - 42 = 0 and II. y² - 17y + 72 = 0, determine the relationship between the values of x and y obtained by solving both equations.

Explanation

Solving equation I: x² - x - 42 = 0 factors as (x - 7)(x + 6) = 0, giving x = 7 or x = -6. Solving equation II: y² - 17y + 72 = 0 factors as (y - 8)(y - 9) = 0, yielding y = 8 or y = 9. Comparing the values, the possible x values are 7 and -6, while y values are 8 and 9. Since both 7 < 8 and -6 < 9, the relationship is x < y.