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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 294 · 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. 1.5x − 3y = 27 and 2x − 5y = 7 →
  2. 2.x + 2y = −17 and 2x + y = −7 →
  3. 3.7x + 9y = 83 and 9x + 7y = 93 →
  4. 4.6x + 3y = 39 and 3x + 6y = 15 →
  5. 5.2x + 8y = 58 and 8x + 2y = 52 →
  6. 6.6x + 5y = 15 and 4x + 4y = 8 →
  7. 7.x + 3y = 14 and 6x − y = −49 →
  8. 8.4x + 6y = −42 and 3x + 6y = −45 →
  9. 9.3x − 6y = −57 and 6x − 6y = −66 →
  10. 10.6x + y = 4 and x + 2y = −14 →
  11. 11.x + 4y = −34 and 4x + y = −1 →
  12. 12.x + 4y = 45 and 6x + y = 63 →
  13. 13.7x + 3y = 45 and 3x + 7y = 65 →
  14. 14.x − 3y = 29 and 3x − 3y = 33 →
  15. 15.7x + 2y = −12 and 2x + 7y = 48 →
  16. 16.3x + 6y = −18 and 6x + 2y = 34 →
  17. 17.4x − 3y = −14 and 2x + 5y = −46 →
  18. 18.4x + 3y = 25 and 2x + 6y = 26 →
  19. 19.2x + 5y = −3 and 4x + 4y = −12 →
  20. 20.4x + y = 32 and 2x − 4y = −20 →
  21. 21.x + 2y = −13 and 2x + 6y = −42 →
  22. 22.5x + 3y = −32 and x + 6y = −1 →
  23. 23.6x + 4y = 54 and 4x + 6y = 56 →
  24. 24.8x + 3y = −23 and 3x + 8y = 12 →
  25. 25.5x − 2y = −17 and 3x + 4y = −31 →
  26. 26.5x + 5y = 20 and 5x + 6y = 21 →
  27. 27.6x + 4y = 2 and 5x + 6y = −17 →
  28. 28.6x + 4y = −8 and 2x + 5y = 12 →
  29. 29.2x + 8y = −60 and 8x + 2y = 0 →
  30. 30.6x + 4y = −18 and 4x + 6y = −32 →
  31. 31.5x + 3y = 21 and 3x + 5y = −13 →
  32. 32.6x + 2y = 14 and 6x + y = 19 →
  33. 33.4x + y = 24 and 5x − 6y = 1 →
  34. 34.9x + 8y = 6 and 8x + 9y = −6 →
  35. 35.3x + 5y = −69 and 6x − 2y = −30 →
  36. 36.9x + y = 37 and x + 9y = 13 →
  37. 37.2x + 5y = 38 and 5x + 2y = 32 →
  38. 38.3x + 3y = −18 and 3x − y = 14 →
  39. 39.3x + 4y = 29 and 3x − 3y = 15 →
  40. 40.7x + 6y = 77 and 6x + 7y = 79 →

Answer key

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

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