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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 334 · 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 − 4y = −4 and 4x + 3y = 17 →
  2. 2.3x + y = −1 and x + 3y = 13 →
  3. 3.7x + 9y = 9 and 9x + 7y = −25 →
  4. 4.x − 5y = −23 and 4x + 4y = 4 →
  5. 5.5x − 5y = 10 and 3x + 5y = −42 →
  6. 6.6x − 5y = −99 and 2x + 4y = 18 →
  7. 7.3x + y = −17 and 2x + 2y = −10 →
  8. 8.2x + 4y = 32 and 4x + 2y = 40 →
  9. 9.4x + y = 45 and 4x − 3y = 9 →
  10. 10.x − 5y = −48 and x + 5y = 32 →
  11. 11.x − y = 2 and 2x + 2y = 12 →
  12. 12.3x − 2y = −37 and 2x + 5y = 26 →
  13. 13.4x + 2y = 28 and 2x + 4y = 8 →
  14. 14.4x − 2y = 0 and x + y = 12 →
  15. 15.3x + 8y = −39 and 8x + 3y = 6 →
  16. 16.6x − 5y = −13 and 2x + 4y = 24 →
  17. 17.3x + y = −13 and x + 4y = 14 →
  18. 18.4x + 4y = 52 and x + 2y = 18 →
  19. 19.2x + 3y = −9 and 3x + 2y = −16 →
  20. 20.2x + 6y = 0 and 3x + 2y = −7 →
  21. 21.3x + 4y = 1 and x + 3y = −8 →
  22. 22.5x − 5y = 0 and 3x − 6y = 24 →
  23. 23.4x + y = 31 and 5x + 5y = 65 →
  24. 24.5x + y = 51 and x + 5y = 39 →
  25. 25.7x + 6y = −16 and 6x + 7y = −10 →
  26. 26.6x − y = 32 and 6x − 4y = 20 →
  27. 27.2x − y = 4 and 5x + 6y = 78 →
  28. 28.6x + 5y = 19 and x − 6y = −31 →
  29. 29.5x + 3y = 5 and 3x + 4y = −8 →
  30. 30.3x + 2y = 13 and 3x − 4y = 1 →
  31. 31.x − 3y = −30 and 6x + y = −9 →
  32. 32.4x + 5y = −43 and x + y = −9 →
  33. 33.5x + 5y = 15 and 3x + y = 5 →
  34. 34.4x − 2y = 10 and 4x + 4y = 4 →
  35. 35.3x − 4y = 31 and x + 3y = 6 →
  36. 36.2x − 2y = −6 and 2x + y = −15 →
  37. 37.6x + 6y = −24 and 5x − 5y = 40 →
  38. 38.2x + 2y = 6 and 4x − 5y = −6 →
  39. 39.6x − 5y = −47 and 4x + 2y = 6 →
  40. 40.5x − 2y = 31 and 2x + 5y = 53 →

Answer key

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

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