Explanation:

Let’s break it down step by step:

- First, solve the first equation: 3x² – 18x + 15 = 0

Divide by 3: x² – 6x + 5 = 0

Factor: (x – 1)(x – 5) = 0, so x = 1 or x = 5

- Now the second equation: 4y² – 84y + 320 = 0

Divide by 4: y² – 21y + 80 = 0

Factor: (y – 16)(y – 5) = 0, so y = 16 or y = 5

Here’s what these numbers tell us:

- Possible x values: 1, 5

- Possible y values: 5, 16

Now, compare all possible pairings:

- If x = 1, y can be 5 or 16 ? x < y

- If x = 5, y can be 5 or 16 ? x = y or x < y

That means x is always less than or equal to y.

So, here’s the bottom line:

Option 2: x = y  is correct.

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For completeness:

- Option 1 (x > y): Never occurs.

- Option 2 (x = y): Always true.

- Option 3 (x = y): Not always true.

- Option 4 (x < y): Not always true (because x = y is possible).

- Option 5 (relation undetermined): We’ve shown the relationship is defined.

Hope that clears it up!