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What is the relationship between $x$ and $y$ if I. $x^{2} - 13 x + 42 = 0$
II. $y^{2} - 10 y + 24 = 0$ ?

Competition practiceQuadratic Comparison

A $x > y$
B $x$ ≤ $y$
C $x$ ≥ $y$
D $x < y$

Step-by-Step Solution

I:

(x - 6) (x - 7) = 0

, so

x = 6

or 7. II:

(y - 4) (y - 6) = 0

, so

y = 4

or 6. The smallest

x

equals the largest

y

(6), so

x

≥

y

.

Answer: C)

x

≥

y

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