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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 527 · 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. 1.3x − 4y = −19 and 6x + 2y = 32 →
  2. 2.x + 3y = −24 and 4x − 6y = 12 →
  3. 3.5x + 8y = 83 and 8x + 5y = 86 →
  4. 4.3x + 4y = 56 and 2x − 2y = 0 →
  5. 5.x + 4y = −19 and x − 6y = 11 →
  6. 6.4x + y = 41 and 4x + 4y = 56 →
  7. 7.x + 5y = −7 and 5x + y = 13 →
  8. 8.2x − 6y = 44 and 4x + 5y = 3 →
  9. 9.4x − 5y = 29 and 2x + 4y = −44 →
  10. 10.2x + 5y = −29 and x + 5y = −37 →
  11. 11.5x + 7y = 52 and 7x + 5y = 68 →
  12. 12.3x + 7y = 8 and 7x + 3y = 32 →
  13. 13.4x + 3y = 23 and 2x + 5y = 29 →
  14. 14.6x + y = −17 and x + 6y = −32 →
  15. 15.9x + 2y = 74 and 2x + 9y = 25 →
  16. 16.5x + 3y = 16 and 2x + 4y = 12 →
  17. 17.5x + 2y = −10 and 4x + 6y = 14 →
  18. 18.2x − 5y = −27 and 6x + 4y = 14 →
  19. 19.4x + 9y = 105 and 9x + 4y = 90 →
  20. 20.2x + 3y = 33 and 3x + 2y = 27 →
  21. 21.5x + 4y = 46 and 6x + 4y = 48 →
  22. 22.6x + 7y = 28 and 7x + 6y = 37 →
  23. 23.4x + 6y = −40 and 6x + 4y = −50 →
  24. 24.x + 4y = −3 and 4x + y = 3 →
  25. 25.4x + 6y = 58 and 6x + 5y = 59 →
  26. 26.8x + 4y = −32 and 4x + 8y = −40 →
  27. 27.5x + 2y = −24 and 2x + 5y = 24 →
  28. 28.2x + y = 4 and x + 3y = −3 →
  29. 29.x + 8y = −27 and 8x + y = 36 →
  30. 30.4x + 3y = −37 and 4x − 3y = −19 →
  31. 31.2x + 6y = −10 and 6x + 2y = 2 →
  32. 32.3x + 6y = 51 and 3x − 2y = 11 →
  33. 33.6x + 3y = −18 and 3x + 6y = −18 →
  34. 34.8x + y = 47 and x + 8y = 61 →
  35. 35.x + 5y = 8 and 3x − 3y = −12 →
  36. 36.x + 6y = 37 and 6x + y = −23 →
  37. 37.6x + 4y = 44 and 4x + 5y = 41 →
  38. 38.3x − 5y = 64 and 3x + 2y = 8 →
  39. 39.7x + 2y = −9 and 2x + 7y = 36 →
  40. 40.2x + 6y = 8 and x − 2y = −6 →

Answer key

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

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