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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 893 · 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 + 3y = 51 and 5x + 5y = 60 →
  2. 2.7x + 6y = −17 and 6x + 7y = −22 →
  3. 3.x − 6y = 42 and x + 6y = −30 →
  4. 4.2x + 5y = −37 and 6x − 4y = −16 →
  5. 5.x + 3y = 23 and 3x + y = 29 →
  6. 6.2x − y = 7 and 6x − y = 31 →
  7. 7.5x + 2y = −13 and 2x + 5y = 20 →
  8. 8.6x + 2y = 58 and 2x + 6y = 46 →
  9. 9.2x + 3y = −7 and 5x + 3y = 5 →
  10. 10.3x + 2y = −1 and x + 6y = 21 →
  11. 11.6x + 5y = 53 and 5x + y = 41 →
  12. 12.4x + 6y = 90 and 6x + 4y = 90 →
  13. 13.9x + 5y = −62 and 5x + 9y = −22 →
  14. 14.6x + 5y = 72 and 3x + 3y = 39 →
  15. 15.6x + 3y = −9 and 3x + 6y = 9 →
  16. 16.9x + 5y = −19 and 5x + 9y = 33 →
  17. 17.2x + 2y = −34 and x − 5y = 37 →
  18. 18.4x − y = 39 and 4x − 5y = 67 →
  19. 19.6x + 4y = 26 and 4x + 6y = 14 →
  20. 20.2x − 2y = 24 and 3x + y = 20 →
  21. 21.5x − 5y = −35 and 6x + y = −21 →
  22. 22.4x + 7y = 29 and 7x + 4y = 59 →
  23. 23.7x + 8y = 41 and 8x + 7y = 34 →
  24. 24.3x − 2y = 23 and 3x + 4y = 17 →
  25. 25.4x + 6y = 38 and 2x + 5y = 25 →
  26. 26.4x + y = 42 and x − y = 3 →
  27. 27.5x + 4y = 45 and 3x + y = 20 →
  28. 28.3x − 2y = 26 and x + y = −3 →
  29. 29.2x + 6y = 36 and 6x + 2y = 44 →
  30. 30.5x + 3y = 22 and 3x + 5y = 10 →
  31. 31.7x + 8y = 105 and 8x + 7y = 105 →
  32. 32.x + y = 15 and 2x + 5y = 57 →
  33. 33.6x + 4y = 6 and 4x + 6y = 24 →
  34. 34.x + 5y = 8 and 3x − 2y = −10 →
  35. 35.6x + y = −34 and x + 4y = 2 →
  36. 36.4x + 2y = −22 and 5x + 6y = −10 →
  37. 37.4x − 3y = −30 and 6x + y = −34 →
  38. 38.5x + 8y = 19 and 8x + 5y = −32 →
  39. 39.4x − 3y = 9 and 4x + 5y = 81 →
  40. 40.8x + 6y = 74 and 6x + 8y = 80 →

Answer key

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

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