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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 471 · 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. 1.2x + 4y = 18 and 4x + 2y = 12 →
  2. 2.4x − y = −12 and 6x + 5y = −70 →
  3. 3.x − 4y = 25 and 5x + 2y = −29 →
  4. 4.9x + 5y = −40 and 5x + 9y = −16 →
  5. 5.2x + 5y = 47 and 6x − y = −3 →
  6. 6.3x + 8y = 61 and 8x + 3y = 16 →
  7. 7.6x + 2y = 4 and x + 2y = −6 →
  8. 8.5x − y = 19 and 4x − y = 17 →
  9. 9.5x − 3y = 64 and 4x + 6y = −16 →
  10. 10.x + 2y = 11 and 2x − 6y = −58 →
  11. 11.4x + 6y = −58 and 6x + 4y = −52 →
  12. 12.6x + 8y = 24 and 8x + 6y = 4 →
  13. 13.6x + 4y = 48 and 4x + 6y = 62 →
  14. 14.5x − 6y = 48 and 3x − 6y = 36 →
  15. 15.4x + 7y = 18 and 7x + 4y = 15 →
  16. 16.3x − 4y = −30 and 6x + 4y = −24 →
  17. 17.x + 2y = 0 and 2x + y = −6 →
  18. 18.6x + 3y = 48 and 3x + 6y = 42 →
  19. 19.9x + 7y = −56 and 7x + 9y = −40 →
  20. 20.6x + 3y = 0 and 6x − 2y = −10 →
  21. 21.4x − 4y = 16 and 4x − y = 22 →
  22. 22.4x + 3y = 20 and 3x + 4y = 29 →
  23. 23.5x + y = 46 and 6x + 2y = 56 →
  24. 24.6x − 6y = −18 and 5x + 4y = 21 →
  25. 25.4x + 3y = −11 and 6x + 6y = −12 →
  26. 26.x + 6y = 19 and 2x + 6y = 14 →
  27. 27.6x + 5y = 47 and 5x + 6y = 52 →
  28. 28.4x + 3y = −9 and 6x + 2y = −16 →
  29. 29.2x + 6y = 20 and 6x + 2y = 44 →
  30. 30.8x + 9y = 62 and 9x + 8y = 57 →
  31. 31.x + 4y = 26 and 4x + y = −1 →
  32. 32.5x + 6y = 57 and 6x + 5y = 64 →
  33. 33.5x − 5y = 15 and x + 5y = −45 →
  34. 34.3x + 4y = −16 and x + 5y = −9 →
  35. 35.5x − 4y = −11 and 5x − 3y = −17 →
  36. 36.4x + y = 13 and x + 4y = 7 →
  37. 37.3x + 4y = 14 and 5x + 6y = 22 →
  38. 38.4x + 4y = 16 and 6x + y = −11 →
  39. 39.x + 2y = 16 and 2x + y = 14 →
  40. 40.x + 3y = 9 and 6x + 5y = 2 →

Answer key

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

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