In each of these questions, two equations (I) and (II) are given. Solve both equations and give the answer. I. $x^2 - 16x + 63 = 0$ II. $y^2 - 21y + 108 = 0$

If x > y
If x ≥ y
If x < y
If x ≤ y

Correct answer: If x ≤ y

Solution

Equation I factors as $(x-7)(x-9)=0$, so $x=7$ or $9$. Equation II factors as $(y-9)(y-12)=0$, so $y=9$ or $12$. In every possible case, $x \le y$ holds.

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