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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 24 · 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 + 2y = 26 and 3x − 3y = −18 →
  2. 2.6x − 3y = −30 and 4x + 3y = 10 →
  3. 3.6x + 3y = 21 and 5x − 2y = 22 →
  4. 4.4x + y = −26 and x + 4y = 16 →
  5. 5.2x + 6y = −6 and x + 4y = −7 →
  6. 6.x + 4y = 17 and 3x + 2y = 11 →
  7. 7.x + 4y = 27 and 4x + y = −27 →
  8. 8.x + 2y = −9 and 2x + y = 6 →
  9. 9.x − 4y = −12 and 5x + 3y = −37 →
  10. 10.5x + 6y = 1 and 5x + 2y = −3 →
  11. 11.x + 2y = 20 and 2x + y = 22 →
  12. 12.6x − 5y = 23 and 5x + 6y = 9 →
  13. 13.x + 7y = 30 and 7x + y = 18 →
  14. 14.x + 3y = 8 and 4x + y = 21 →
  15. 15.3x − 5y = 45 and 4x − 3y = 38 →
  16. 16.3x − 5y = −66 and 6x + 3y = −15 →
  17. 17.x + 5y = −7 and 5x + y = 13 →
  18. 18.5x + 6y = 60 and x + 3y = 21 →
  19. 19.2x + y = 13 and x + 2y = 17 →
  20. 20.6x + 5y = 63 and 4x + y = 35 →
  21. 21.8x + y = −48 and x + 8y = 57 →
  22. 22.3x + 5y = 54 and 5x + 3y = 58 →
  23. 23.x + 4y = 32 and 3x + 3y = 33 →
  24. 24.4x + 4y = 8 and 3x + 2y = 10 →
  25. 25.x + 5y = 11 and 6x + y = 8 →
  26. 26.4x − 2y = 14 and x + 6y = 36 →
  27. 27.2x − 2y = 12 and 2x − 4y = 26 →
  28. 28.6x + 6y = 78 and x + 3y = 29 →
  29. 29.x + 6y = 55 and 4x − 4y = −32 →
  30. 30.x − 2y = −15 and 6x − 2y = −40 →
  31. 31.3x − 6y = −45 and x + 6y = 49 →
  32. 32.x − 2y = −13 and 3x + y = 17 →
  33. 33.7x + 8y = −15 and 8x + 7y = −30 →
  34. 34.x + 6y = 46 and 5x + 4y = 22 →
  35. 35.2x + 6y = 34 and 6x + 2y = −26 →
  36. 36.9x + 4y = 79 and 4x + 9y = 64 →
  37. 37.5x + 6y = −21 and 4x − 4y = 36 →
  38. 38.2x − 5y = −3 and x − 4y = −6 →
  39. 39.3x + 4y = −19 and 4x + 3y = −23 →
  40. 40.x − 3y = −7 and x + 5y = 17 →

Answer key

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

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