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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 150 · 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. 1.5x + y = −7 and 4x − 3y = −36 →
  2. 2.9x + y = 29 and x + 9y = 21 →
  3. 3.3x − 3y = −6 and 4x − 5y = −12 →
  4. 4.2x + y = 8 and x + 2y = 10 →
  5. 5.2x − 5y = −7 and 6x + 2y = 30 →
  6. 6.7x + 3y = 49 and 3x + 7y = 61 →
  7. 7.2x + 3y = 20 and 3x + 2y = 25 →
  8. 8.x − y = −13 and 6x + 6y = 6 →
  9. 9.x + 6y = −13 and 5x − 2y = −33 →
  10. 10.5x + 5y = −70 and 4x + 5y = −64 →
  11. 11.5x + 4y = 30 and 4x + 5y = 33 →
  12. 12.4x + y = 10 and 6x − 3y = 42 →
  13. 13.5x + 6y = 40 and 6x + 5y = 37 →
  14. 14.5x + 3y = 3 and 4x + y = 15 →
  15. 15.x + 9y = 36 and 9x + y = 84 →
  16. 16.2x + y = 11 and x + 2y = −2 →
  17. 17.6x + y = 12 and 6x + 6y = −18 →
  18. 18.3x + 3y = 18 and 3x + 5y = 28 →
  19. 19.7x + 9y = 77 and 9x + 7y = 67 →
  20. 20.4x + 9y = −95 and 9x + 4y = −100 →
  21. 21.x + 7y = 62 and 7x + y = 2 →
  22. 22.2x − 5y = 3 and 5x + 5y = 60 →
  23. 23.4x − 3y = 51 and 5x + 5y = −15 →
  24. 24.2x + 2y = 24 and 3x − 4y = −6 →
  25. 25.3x + 2y = 19 and 6x + 5y = 46 →
  26. 26.x + 2y = −10 and 2x + y = 7 →
  27. 27.4x + 5y = 56 and 5x − 4y = 29 →
  28. 28.x + 5y = 46 and x + 6y = 54 →
  29. 29.5x + 2y = 47 and 2x + 2y = 20 →
  30. 30.2x + 4y = 38 and 2x − y = −7 →
  31. 31.x + 2y = 0 and 2x + y = −6 →
  32. 32.3x + 4y = −5 and 4x + 3y = −9 →
  33. 33.6x − 3y = 54 and 4x + 5y = −20 →
  34. 34.6x + 5y = −73 and 5x + 5y = −65 →
  35. 35.5x − 6y = −66 and 5x + 3y = −12 →
  36. 36.4x + 3y = 18 and 6x + y = 20 →
  37. 37.4x − 2y = −40 and 2x + 4y = 10 →
  38. 38.5x + y = 32 and x + 5y = 16 →
  39. 39.6x + 6y = −18 and 6x + 5y = −9 →
  40. 40.x + 8y = 8 and 8x + y = −62 →

Answer key

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

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