**Given:**

(i) $ x^2 - 5x + 6 = 0 $

(ii) $ 3y^2 + 3y - 18 = 0 $

**Question:**

Based on the above equations, determine the correct relationship between $ x $ and $ y $.

Question

**Given:**

(i) $ x^2 - 5x + 6 = 0 $

(ii) $ 3y^2 + 3y - 18 = 0 $

**Question:**

Based on the above equations, determine the correct relationship between $ x $ and $ y $.

Accepted Answer

**Solution:**

1. Solve the first quadratic equation:

$$
x^2 - 5x + 6 = 0
$$

Factorizing:

$$
(x - 2)(x - 3) = 0
$$

So, $ x = 2 $ or $ x = 3 $.

2. Solve the second quadratic equation:

$$
3y^2 + 3y - 18 = 0
$$

Divide throughout by 3:

$$
y^2 + y - 6 = 0
$$

Factorizing:

$$
(y + 3)(y - 2) = 0
$$

So, $ y = -3 $ or $ y = 2 $.

3. Now, compare possible values of $ x $ and $ y $:

- If $ x = 2 $ and $ y = 2 $, then $ x = y $.
- If $ x = 3 $ and $ y = 2 $, then $ x > y $.
- If $ x = 2 $ and $ y = -3 $, then $ x > y $.
- If $ x = 3 $ and $ y = -3 $, then $ x > y $.

4. Since $ x $ can be equal to or greater than $ y $, the correct relationship is:

$$
x \geq y
$$

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

Answer

Answer

Answer