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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 428 · 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. 1.6x − 4y = −48 and 2x − y = −15 →
  2. 2.5x − 5y = −45 and 4x + 4y = −28 →
  3. 3.6x + 3y = −12 and 3x + 6y = 30 →
  4. 4.6x + 4y = 38 and 4x + 6y = 22 →
  5. 5.6x + 3y = −9 and x − 2y = 21 →
  6. 6.x + 9y = −80 and 9x + y = −80 →
  7. 7.6x + 4y = 80 and 4x + 6y = 80 →
  8. 8.9x + 6y = 123 and 6x + 9y = 117 →
  9. 9.8x + 6y = 70 and 6x + 8y = 56 →
  10. 10.9x + 3y = 105 and 3x + 9y = 99 →
  11. 11.2x − 6y = −64 and x + 4y = 31 →
  12. 12.4x + 6y = 82 and 6x + 4y = 78 →
  13. 13.2x + 3y = 10 and 6x + 6y = 18 →
  14. 14.x − 6y = −27 and 2x − 6y = −24 →
  15. 15.x + y = 3 and x + 2y = 4 →
  16. 16.9x + 6y = 99 and 6x + 9y = 81 →
  17. 17.x − 4y = −12 and 5x + 2y = −16 →
  18. 18.4x + 2y = 0 and 4x + 5y = 6 →
  19. 19.3x + 5y = 24 and 5x + 3y = 8 →
  20. 20.3x + 4y = 40 and 6x − 6y = 24 →
  21. 21.2x − 6y = −20 and 2x + y = 22 →
  22. 22.x + 2y = −8 and 2x + y = 5 →
  23. 23.7x + 3y = −47 and 3x + 7y = −43 →
  24. 24.2x − 2y = −8 and x + 6y = 59 →
  25. 25.4x − 2y = 4 and 3x + y = 13 →
  26. 26.2x + 3y = 25 and 6x + y = 3 →
  27. 27.4x + 4y = −8 and 5x + 2y = −1 →
  28. 28.2x + y = 5 and x + 2y = 7 →
  29. 29.2x − 3y = 5 and x − 2y = 5 →
  30. 30.4x + 9y = 26 and 9x + 4y = −39 →
  31. 31.4x + y = −14 and 6x + 2y = −18 →
  32. 32.4x − 4y = −8 and 2x + 2y = −12 →
  33. 33.7x + y = 33 and x + 7y = 39 →
  34. 34.6x + 6y = 30 and 6x − y = 51 →
  35. 35.x − 2y = 16 and 6x − 5y = 61 →
  36. 36.5x + 6y = 9 and 6x + 5y = 24 →
  37. 37.2x + 3y = −31 and 2x − 6y = 32 →
  38. 38.x + 5y = −37 and x + 2y = −13 →
  39. 39.4x − y = 42 and 6x − 3y = 72 →
  40. 40.6x + 2y = −30 and 2x + 6y = 22 →

Answer key

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

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