In each of the following questions, two equations (I) and (II) are given. Solve both the equations and determine the correct relationship between *x* and *y*.

**Q:**

I. $ x - \sqrt{169} = 0 $

II. $ y^2 - 169 = 0 $

Choose the correct option:

Question

In each of the following questions, two equations (I) and (II) are given. Solve both the equations and determine the correct relationship between *x* and *y*.

**Q:**

I. $ x - \sqrt{169} = 0 $

II. $ y^2 - 169 = 0 $

Choose the correct option:

Accepted Answer

**Solution:**

1. From equation (I):
   $$
   x - \sqrt{169} = 0 \implies x = \sqrt{169} = 13
   $$

2. From equation (II):
   $$
   y^2 - 169 = 0 \implies y^2 = 169 \implies y = \pm 13
   $$

3. Now, compare *x* and *y*:
   - Since $ x = 13 $
   - $ y $ can be either $ 13 $ or $ -13 $

4. When $ y = 13 $, $ x = y $.

5. When $ y = -13 $, $ x > y $.

6. Therefore, the relationship $ x \geq y $ always holds true.

**Answer:** (b) $ x \geq y $

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