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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 687 · 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 + 5y = 31 and 5x + 3y = 25 →
  2. 2.5x + 2y = 37 and 4x − y = 40 →
  3. 3.6x + 6y = 36 and 5x − 3y = −42 →
  4. 4.4x + 3y = 33 and 3x + 4y = 23 →
  5. 5.x + 6y = 19 and x + 5y = 15 →
  6. 6.2x + 2y = 10 and 6x + y = 15 →
  7. 7.6x − 4y = 16 and 3x + y = 5 →
  8. 8.x + 4y = −23 and 4x + 5y = −37 →
  9. 9.3x + 8y = −84 and 8x + 3y = −59 →
  10. 10.x + 4y = 9 and 4x + y = 21 →
  11. 11.4x + 6y = −48 and 6x + 4y = −52 →
  12. 12.4x + 5y = 61 and 5x + 4y = 56 →
  13. 13.4x − 5y = 56 and x − 2y = 17 →
  14. 14.6x − 2y = 52 and 2x + 5y = 23 →
  15. 15.x − y = −5 and 6x − 2y = −2 →
  16. 16.6x + y = 15 and 3x + 5y = −33 →
  17. 17.3x − y = 21 and 2x − 3y = 0 →
  18. 18.8x + 6y = 42 and 6x + 8y = 14 →
  19. 19.x + 6y = 6 and 2x + y = −10 →
  20. 20.5x + 2y = 31 and 4x + 5y = 18 →
  21. 21.6x − 2y = 62 and 3x − 5y = 59 →
  22. 22.5x + 3y = 15 and x + 3y = −9 →
  23. 23.2x + 8y = 52 and 8x + 2y = 28 →
  24. 24.6x − 4y = −50 and 5x + 4y = −5 →
  25. 25.5x + 6y = −28 and 4x + 5y = −24 →
  26. 26.9x + 3y = 12 and 3x + 9y = 12 →
  27. 27.2x + 5y = 56 and x − 2y = −8 →
  28. 28.2x + 8y = −62 and 8x + 2y = −68 →
  29. 29.5x + 5y = 0 and x + 4y = 12 →
  30. 30.6x + y = −7 and x + 6y = 28 →
  31. 31.7x + 2y = 70 and 2x + 7y = 65 →
  32. 32.2x − 6y = 26 and x − 6y = 28 →
  33. 33.6x + y = −11 and 4x + y = −5 →
  34. 34.2x + 7y = 32 and 7x + 2y = 67 →
  35. 35.5x + y = 34 and x − 3y = −6 →
  36. 36.5x − 6y = 67 and x + 6y = −37 →
  37. 37.5x − 5y = 80 and x + 2y = −11 →
  38. 38.4x − 5y = −29 and 5x + 3y = 10 →
  39. 39.3x + 9y = 51 and 9x + 3y = 9 →
  40. 40.6x + 5y = 64 and 5x + 6y = 57 →

Answer key

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

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