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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 405 · 40 sums
TalentJR

The trick (Paravartya Yojayet): For ax + by = c and dx + ey = f: bottom = a×e − b×d. x = (c×e − b×f) ÷ bottom; y = (a×f − c×d) ÷ bottom. Special case ax + by = c, bx + ay = f: add the equations to get x + y, subtract to get x − y, then add and halve. Check your x and y in the first equation.

NameDateTime takenScore ___ / 40
  1. 1.4x − 5y = −17 and 2x + 4y = 50 →
  2. 2.2x + y = 1 and x + 2y = −10 →
  3. 3.x + 7y = −13 and 7x + y = −43 →
  4. 4.4x + 4y = −16 and 6x − y = −17 →
  5. 5.3x + y = −24 and x − 4y = −21 →
  6. 6.2x + 5y = −1 and 5x + 2y = 29 →
  7. 7.4x + 5y = 32 and 2x + 4y = 28 →
  8. 8.3x + y = 21 and x + 3y = 15 →
  9. 9.2x − 3y = −13 and 3x − 6y = −24 →
  10. 10.7x + 9y = 65 and 9x + 7y = 79 →
  11. 11.3x − 5y = 20 and 2x − 5y = 25 →
  12. 12.2x + 6y = 30 and 6x + 2y = 58 →
  13. 13.x − 4y = 38 and 3x + y = −3 →
  14. 14.2x + 4y = −14 and 6x + 4y = −18 →
  15. 15.4x + 3y = 34 and 3x + 4y = 29 →
  16. 16.6x + 4y = 14 and 4x + 4y = 4 →
  17. 17.6x + 8y = 58 and 8x + 6y = 54 →
  18. 18.5x + 2y = 32 and 6x + 2y = 36 →
  19. 19.x + 3y = −16 and 5x − 5y = 0 →
  20. 20.2x + 2y = 20 and 4x + y = 31 →
  21. 21.x + y = 11 and 2x + 6y = 50 →
  22. 22.4x − y = −25 and 5x + 2y = −28 →
  23. 23.4x − 2y = 20 and 2x − 2y = 6 →
  24. 24.4x + 4y = −48 and 4x + y = −24 →
  25. 25.3x + y = −17 and x + 3y = −3 →
  26. 26.6x + 2y = −18 and 5x − 6y = −61 →
  27. 27.2x + 7y = 13 and 7x + 2y = −22 →
  28. 28.8x + 6y = −20 and 6x + 8y = 6 →
  29. 29.9x + 2y = −73 and 2x + 9y = −59 →
  30. 30.2x − 4y = −10 and x + y = 7 →
  31. 31.7x + 6y = 85 and 6x + 7y = 84 →
  32. 32.4x + 6y = 24 and 4x + 4y = 28 →
  33. 33.2x − 3y = 11 and 5x − y = 8 →
  34. 34.7x + y = 33 and x + 7y = −57 →
  35. 35.4x + y = 27 and 3x + 2y = 14 →
  36. 36.4x + 6y = 34 and 3x − y = −24 →
  37. 37.3x + 4y = 14 and x − 3y = −30 →
  38. 38.5x − 2y = 8 and 6x − 3y = 6 →
  39. 39.7x + 4y = 25 and 4x + 7y = 19 →
  40. 40.x + 3y = −3 and 3x + y = 23 →

Answer key

  1. x = 7, y = 9
  2. x = 4, y = −7
  3. x = −6, y = −1
  4. x = −3, y = −1
  5. x = −9, y = 3
  6. x = 7, y = −3
  7. x = −2, y = 8
  8. x = 6, y = 3
  9. x = −2, y = 3
  10. x = 8, y = 1
  11. x = −5, y = −7
  12. x = 9, y = 2
  13. x = 2, y = −9
  14. x = −1, y = −3
  15. x = 7, y = 2
  16. x = 5, y = −4
  17. x = 3, y = 5
  18. x = 4, y = 6
  19. x = −4, y = −4
  20. x = 7, y = 3
  21. x = 4, y = 7
  22. x = −6, y = 1
  23. x = 7, y = 4
  24. x = −4, y = −8
  25. x = −6, y = 1
  26. x = −5, y = 6
  27. x = −4, y = 3
  28. x = −7, y = 6
  29. x = −7, y = −5
  30. x = 3, y = 4
  31. x = 7, y = 6
  32. x = 9, y = −2
  33. x = 1, y = −3
  34. x = 6, y = −9
  35. x = 8, y = −5
  36. x = −5, y = 9
  37. x = −6, y = 8
  38. x = 4, y = 6
  39. x = 3, y = 1
  40. x = 9, y = −4

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