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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 303 · 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.x + 4y = 39 and 4x + y = 36 →
  2. 2.2x + 4y = 14 and x + 3y = 8 →
  3. 3.x − 2y = −3 and 2x + 2y = 6 →
  4. 4.5x + 9y = 46 and 9x + 5y = −18 →
  5. 5.3x − 2y = 15 and 3x + 4y = 33 →
  6. 6.3x + 2y = 19 and 5x + 4y = 37 →
  7. 7.6x − 4y = 58 and 6x − y = 37 →
  8. 8.2x − 3y = 41 and 3x + 5y = −24 →
  9. 9.7x + y = 41 and x + 7y = 47 →
  10. 10.4x − 2y = 6 and 5x + 4y = 66 →
  11. 11.x + 2y = −4 and 2x + y = 1 →
  12. 12.9x + 4y = −10 and 4x + 9y = −55 →
  13. 13.4x + 8y = 60 and 8x + 4y = 84 →
  14. 14.8x + 6y = 50 and 6x + 8y = 48 →
  15. 15.x + y = 2 and 6x + 5y = 11 →
  16. 16.4x + y = −13 and 4x + 2y = −10 →
  17. 17.2x + 5y = 38 and 4x − 4y = 20 →
  18. 18.8x + 6y = 44 and 6x + 8y = 54 →
  19. 19.5x + 5y = 70 and 3x − y = 18 →
  20. 20.3x + 3y = 3 and 4x + y = 13 →
  21. 21.5x + 3y = 56 and 6x − 5y = 7 →
  22. 22.5x + 5y = 45 and 3x − 2y = −3 →
  23. 23.4x + 3y = 31 and 4x − 6y = −14 →
  24. 24.6x + 2y = 20 and 2x + 6y = −36 →
  25. 25.6x − y = −7 and 2x − 4y = −6 →
  26. 26.x + 4y = 19 and 4x + y = 16 →
  27. 27.x − y = −7 and 6x − 3y = −27 →
  28. 28.6x − 4y = −46 and 5x + 4y = −53 →
  29. 29.6x − 3y = 66 and 2x + 3y = 6 →
  30. 30.2x + 6y = −30 and 6x + 2y = −42 →
  31. 31.2x + 8y = 26 and 8x + 2y = 74 →
  32. 32.6x − 2y = −10 and 3x + 3y = −33 →
  33. 33.2x − 3y = −33 and 5x − 3y = −42 →
  34. 34.9x + y = 89 and x + 9y = 81 →
  35. 35.6x − 4y = 0 and 2x + 4y = 32 →
  36. 36.x + 3y = 17 and 5x + 6y = 49 →
  37. 37.4x − 3y = −47 and 5x + 2y = −7 →
  38. 38.7x + 6y = −63 and 6x + 7y = −67 →
  39. 39.x − 6y = −7 and 5x + 2y = −3 →
  40. 40.2x + 4y = 40 and 4x + 2y = 32 →

Answer key

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

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