Multiple choice

In the following questions two equations I and II are given. You have to solve both the equations and give answer. $( (I) \quad x^2 + y^2 = 45 \qquad (II) \quad x + y = 9 )$

  1. If x > y

  2. If x ≥ y

  3. If x < y

  4. If x ≤ y

  5. If x = y or the relationship cannot be determined
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E Correct answer
Explanation

From (II), y = 9 - x. Substitute into (I): x² + (9-x)² = 45 gives x² + 81 - 18x + x² = 45, so 2x² - 18x + 36 = 0, which simplifies to x² - 9x + 18 = 0. This gives x = 3 or x = 6. When x = 3, y = 6. When x = 6, y = 3. Since x can be greater than, less than, or equal to y depending on which solution we take, the relationship cannot be uniquely determined.

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