Solve the simultaneous equation 3x – y = 3 and 9x² – y² = 45

JAMB Mathematics 2024 209 views
Source: JAMB · 2024

Solve the simultaneous equation 3x – y = 3 and 9x² – y² = 45

  1. x = 2 and y = -3
  2. x = 3 and y = 6 ✓
  3. x = 1 and y = 3
  4. x = -3 and y = 4
Explanation

Factorise the second equation: 9x² – y² = (3x – y)(3x + y) = 45.

Since 3x – y = 3, we get 3(3x + y) = 45, so 3x + y = 15.

Add this to 3x – y = 3: 6x = 18, so x = 3. Then y = 3x – 3 = 6. So x = 3 and y = 6. Check: 81 – 36 = 45.

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