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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 372 · 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.x + 9y = 75 and 9x + y = 35 →
  2. 2.6x + 3y = −6 and 2x − 5y = −38 →
  3. 3.9x + y = −37 and x + 9y = −13 →
  4. 4.2x + 7y = 28 and 7x + 2y = −37 →
  5. 5.2x + 7y = −3 and 7x + 2y = 57 →
  6. 6.5x + 8y = 83 and 8x + 5y = 86 →
  7. 7.6x − 5y = −67 and 2x + 6y = 16 →
  8. 8.x + 2y = 3 and 2x − 4y = −2 →
  9. 9.4x − 3y = 23 and 4x − 5y = 17 →
  10. 10.7x + 2y = 15 and 2x + 7y = 30 →
  11. 11.x + 9y = 76 and 9x + y = −36 →
  12. 12.2x + 3y = 29 and 2x + y = 11 →
  13. 13.6x + 7y = −71 and 7x + 6y = −72 →
  14. 14.6x + 3y = 63 and 2x + 4y = 36 →
  15. 15.5x − 6y = −59 and 3x − 3y = −30 →
  16. 16.2x + 9y = 24 and 9x + 2y = 31 →
  17. 17.2x − 3y = −15 and 3x + y = −17 →
  18. 18.x + 4y = −30 and 4x + y = −15 →
  19. 19.x + 4y = 9 and 4x + y = −24 →
  20. 20.6x − 6y = −18 and 6x + 2y = 46 →
  21. 21.4x + 5y = 59 and 5x + y = 37 →
  22. 22.2x + 4y = 4 and 4x + 3y = 23 →
  23. 23.x + 4y = 13 and 2x + 2y = 14 →
  24. 24.7x + 4y = 50 and 4x + 7y = 71 →
  25. 25.6x + 5y = 1 and 2x + y = 1 →
  26. 26.4x + 4y = 60 and 5x − 4y = 12 →
  27. 27.x + 6y = −24 and 3x − 4y = 38 →
  28. 28.2x − 4y = −20 and x + 5y = −3 →
  29. 29.2x + 6y = −48 and 6x + 5y = −66 →
  30. 30.3x + 2y = −22 and 4x + 3y = −32 →
  31. 31.9x + 2y = −56 and 2x + 9y = 56 →
  32. 32.2x + y = 17 and x + 2y = 10 →
  33. 33.9x + y = 28 and x + 9y = 12 →
  34. 34.2x + 4y = −14 and 4x + 2y = −16 →
  35. 35.2x + 6y = 38 and 5x + y = −17 →
  36. 36.5x − y = 31 and x + y = 5 →
  37. 37.5x − 4y = 32 and 4x + 3y = 7 →
  38. 38.x + 2y = −21 and 2x + y = −15 →
  39. 39.x − 4y = 9 and x + 6y = −31 →
  40. 40.x + 3y = 24 and 3x + y = 32 →

Answer key

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

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