Given the two equations:

I. $ x^2 = 81 $

II. $ (y - 9)^2 = 0 $

Determine the correct relationship between $ x $ and $ y $.

Question

Given the two equations:

I. $ x^2 = 81 $

II. $ (y - 9)^2 = 0 $

Determine the correct relationship between $ x $ and $ y $.

Accepted Answer

**Solution:**

1. From equation I: $ x^2 = 81 $
   - Taking square root on both sides, we get $ x = +- 9 $.

2. From equation II: $ (y - 9)^2 = 0 $
   - This implies $ y - 9 = 0 $, so $ y = 9 $.

3. Now, comparing $ x $ and $ y $:
   - $ x $ can be either $ 9 $ or $ -9 $.
   - $ y = 9 $.

4. When $ x = 9 $, $ x = y $.
   When $ x = -9 $, $ x < y $.

Hence, $ y $ is always greater than or equal to $ x $.

**Answer:**

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