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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 510 · 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 − y = 52 and x − 2y = 5 →
  2. 2.x + 3y = 19 and 4x − 6y = −14 →
  3. 3.3x + y = −16 and x + 3y = 0 →
  4. 4.x + 3y = 20 and 3x + y = 20 →
  5. 5.5x + y = 12 and 4x + y = 10 →
  6. 6.x − y = 7 and 5x + 5y = 55 →
  7. 7.7x + 9y = 121 and 9x + 7y = 119 →
  8. 8.x + 4y = 32 and 6x + 4y = 52 →
  9. 9.5x − y = 15 and 2x + y = 13 →
  10. 10.6x + 9y = 108 and 9x + 6y = 102 →
  11. 11.6x + y = 20 and 3x + 3y = 15 →
  12. 12.6x + 2y = 34 and 2x + y = 12 →
  13. 13.9x + 3y = 21 and 3x + 9y = 39 →
  14. 14.3x − 3y = 3 and 6x + 6y = 78 →
  15. 15.8x + 4y = 56 and 4x + 8y = 52 →
  16. 16.6x + 6y = −12 and x − 4y = 28 →
  17. 17.2x + 3y = 20 and 6x − 6y = 0 →
  18. 18.8x + 9y = 31 and 9x + 8y = 37 →
  19. 19.x − 3y = −10 and 2x + 3y = 16 →
  20. 20.6x + 4y = −24 and 6x + 6y = −42 →
  21. 21.9x + 3y = −45 and 3x + 9y = 57 →
  22. 22.4x − 4y = 12 and x − 3y = −3 →
  23. 23.6x + 5y = −19 and 5x + 6y = −25 →
  24. 24.3x − 3y = 6 and 4x + 2y = 14 →
  25. 25.3x + 3y = 30 and 3x + y = 20 →
  26. 26.7x + 2y = 45 and 2x + 7y = 0 →
  27. 27.6x − y = −54 and 3x − 4y = −48 →
  28. 28.2x + 6y = 56 and 5x − 6y = −49 →
  29. 29.2x − y = 9 and 2x + 4y = 24 →
  30. 30.6x + 2y = −6 and 4x − 2y = 16 →
  31. 31.x + 3y = −30 and 3x + y = −26 →
  32. 32.5x + 6y = 43 and 5x + 5y = 35 →
  33. 33.3x + 9y = 57 and 9x + 3y = 75 →
  34. 34.4x − y = 12 and 5x − y = 17 →
  35. 35.x + 9y = 46 and 9x + y = −66 →
  36. 36.5x + 8y = 39 and 8x + 5y = 39 →
  37. 37.6x + 6y = 24 and 2x + 5y = 26 →
  38. 38.7x + 4y = 55 and 4x + 7y = 55 →
  39. 39.5x + 9y = 14 and 9x + 5y = 14 →
  40. 40.6x + 4y = 28 and 4x + 6y = 12 →

Answer key

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

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