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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 733 · 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. 1.2x + 7y = 52 and 7x + 2y = 47 →
  2. 2.4x + 3y = 18 and 5x + 4y = 21 →
  3. 3.7x + 6y = 39 and 6x + 7y = 39 →
  4. 4.3x + y = 14 and 4x − 4y = 56 →
  5. 5.2x − 6y = −8 and 2x − 2y = 0 →
  6. 6.8x + 6y = −2 and 6x + 8y = 30 →
  7. 7.x + 5y = 14 and x − y = 2 →
  8. 8.6x + 5y = 40 and 5x + 4y = 33 →
  9. 9.2x + 9y = 83 and 9x + 2y = 27 →
  10. 10.4x + 2y = 46 and x − y = 1 →
  11. 11.8x + y = −16 and x + 8y = 61 →
  12. 12.2x + 5y = −6 and 2x − 6y = −28 →
  13. 13.3x + 2y = 0 and 2x + 3y = 10 →
  14. 14.2x + 3y = 7 and 3x + 6y = 21 →
  15. 15.3x + 6y = 36 and 6x + 3y = 45 →
  16. 16.2x + 4y = −2 and 3x + y = 22 →
  17. 17.3x + 5y = 42 and 2x + 4y = 32 →
  18. 18.9x + 8y = −23 and 8x + 9y = −28 →
  19. 19.7x + 3y = −21 and 3x + 7y = 31 →
  20. 20.4x + y = 9 and 4x + 2y = 10 →
  21. 21.2x + 8y = 68 and 8x + 2y = 2 →
  22. 22.9x + 3y = −63 and 3x + 9y = 3 →
  23. 23.4x + 3y = −6 and 2x − 3y = 24 →
  24. 24.4x + y = 13 and 3x − 5y = 27 →
  25. 25.x − 6y = 3 and 2x + 4y = 22 →
  26. 26.7x + 3y = −24 and 3x + 7y = −16 →
  27. 27.8x + 7y = 87 and 7x + 8y = 93 →
  28. 28.2x + 6y = −20 and 2x − 2y = 28 →
  29. 29.5x + 8y = 44 and 8x + 5y = 47 →
  30. 30.5x + y = 6 and x + y = 2 →
  31. 31.5x + y = 54 and 3x + 5y = 72 →
  32. 32.6x + 6y = −24 and 2x + 6y = −16 →
  33. 33.2x + 5y = −25 and 3x + 2y = −21 →
  34. 34.6x + 7y = 66 and 7x + 6y = 64 →
  35. 35.2x + 3y = −34 and 3x + 2y = −36 →
  36. 36.4x + 3y = 21 and 3x − 4y = 22 →
  37. 37.6x + 5y = 42 and x − 4y = −22 →
  38. 38.x + 4y = 32 and 4x + y = 23 →
  39. 39.2x − 3y = 27 and 5x − 6y = 57 →
  40. 40.5x − 2y = 50 and 6x − 3y = 63 →

Answer key

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

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