Multiple choice

Directions: In the following question, two equations numbered I and II are given. You have to solve both the equations and give answer. I. x2 - 9x + 10 = -8 II. y2 - 18y + 60 = -20

  1. if x > y

  2. if x ≥ y

  3. if x < y

  4. if x ≤ y

  5. if x = y or Cannot be determined
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Equation I: x^2 - 9x + 18 = 0, so (x-3)(x-6)=0, x=3 or 6. Equation II: y^2 - 18y + 80 = 0, so (y-8)(y-10)=0, y=8 or 10. Comparing all pairs, x is always less than y.

AI explanation

Rearranging the equations yields x2 - 9x + 18 = 0 and y2 - 18y + 80 = 0. Factoring the first gives (x - 3)(x - 6) = 0, so x equals 3 or 6. Factoring the second gives (y - 8)(y - 10) = 0, so y equals 8 or 10. Since both possible values for x are strictly less than both possible values for y, the relationship is x < y.

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