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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 836 · 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 + 3y = −8 and 6x + 2y = 4 →
  2. 2.9x + 3y = 84 and 3x + 9y = 36 →
  3. 3.5x − 4y = 37 and 2x + 3y = −22 →
  4. 4.5x + 6y = 81 and 5x − 5y = 15 →
  5. 5.5x + 4y = 46 and 6x − 5y = −33 →
  6. 6.x + 6y = −62 and 2x + 4y = −52 →
  7. 7.4x − y = 21 and 6x + 3y = 9 →
  8. 8.6x + 3y = 3 and 6x + y = 21 →
  9. 9.4x + 5y = −12 and 5x + 4y = 3 →
  10. 10.8x + y = −1 and x + 8y = −71 →
  11. 11.x + 7y = 36 and 7x + y = 12 →
  12. 12.6x + 4y = 56 and 2x + 4y = 32 →
  13. 13.x + 2y = 14 and 4x + 4y = 24 →
  14. 14.x − 4y = 13 and x + 3y = −1 →
  15. 15.x + 4y = −40 and 4x + y = −40 →
  16. 16.3x + 6y = −27 and 4x + 6y = −24 →
  17. 17.2x + 8y = 28 and 8x + 2y = −8 →
  18. 18.6x + y = 12 and 4x − 6y = −32 →
  19. 19.5x + 6y = 11 and 6x − 6y = 0 →
  20. 20.4x + 4y = −12 and 6x + y = −13 →
  21. 21.4x + y = 30 and x + 4y = 15 →
  22. 22.2x + 3y = 32 and 6x − 6y = 6 →
  23. 23.5x − 4y = −49 and 3x + 5y = −22 →
  24. 24.4x + 5y = −1 and 3x + 6y = −3 →
  25. 25.4x + y = 20 and 4x + 2y = 16 →
  26. 26.x + y = 14 and 3x − y = 10 →
  27. 27.4x + 6y = 54 and 6x + y = 25 →
  28. 28.6x − y = −48 and 6x + 4y = −18 →
  29. 29.8x + y = 25 and x + 8y = 11 →
  30. 30.4x + 7y = 6 and 7x + 4y = −6 →
  31. 31.3x − y = −8 and 5x + y = −8 →
  32. 32.5x + 2y = −23 and x + 2y = −19 →
  33. 33.x + 6y = 52 and 5x + 4y = 52 →
  34. 34.2x − 5y = 13 and 2x + 2y = 20 →
  35. 35.5x + y = −19 and x + 5y = 25 →
  36. 36.5x − 5y = 5 and x − 4y = −5 →
  37. 37.3x − 3y = 18 and 6x + 3y = −27 →
  38. 38.6x − 3y = −6 and 2x + 6y = 40 →
  39. 39.2x + 3y = 27 and 3x + 2y = 23 →
  40. 40.7x + 4y = −65 and 4x + 7y = −56 →

Answer key

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

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