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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 332 · 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. 1.4x + y = −5 and 5x + 5y = 5 →
  2. 2.9x + 6y = 72 and 6x + 9y = 78 →
  3. 3.3x + 3y = 24 and 5x − y = 46 →
  4. 4.3x + 8y = 88 and 8x + 3y = 88 →
  5. 5.x + 4y = 25 and 4x + y = 10 →
  6. 6.4x + 6y = −56 and 6x + 4y = −64 →
  7. 7.x − 2y = 0 and 4x − 3y = 5 →
  8. 8.x + y = 16 and 3x + 6y = 69 →
  9. 9.x − 4y = 21 and x + y = 1 →
  10. 10.2x + y = 16 and x + 2y = 14 →
  11. 11.2x + 6y = 56 and 2x − 6y = −40 →
  12. 12.x + 5y = −42 and 5x − y = −28 →
  13. 13.7x + 3y = 30 and 3x + 7y = 30 →
  14. 14.4x + 3y = 34 and 3x + 4y = 36 →
  15. 15.4x + 6y = 26 and 3x + 5y = 21 →
  16. 16.5x + 9y = −50 and 9x + 5y = −34 →
  17. 17.2x + 3y = 15 and 3x − y = 6 →
  18. 18.4x − y = 30 and 4x + 3y = 6 →
  19. 19.x − 5y = −29 and 3x − 3y = −3 →
  20. 20.2x + 2y = 4 and 6x − 6y = −84 →
  21. 21.5x − 4y = −48 and 2x − y = −15 →
  22. 22.x + 9y = 82 and 9x + y = 18 →
  23. 23.6x + 4y = 18 and 4x + 6y = 22 →
  24. 24.3x − 3y = 33 and 3x − y = 15 →
  25. 25.x + 5y = −23 and 5x + y = 29 →
  26. 26.x + 3y = 12 and 2x + 4y = 14 →
  27. 27.7x + 5y = 6 and 5x + 7y = 18 →
  28. 28.5x − 3y = −1 and 4x + 5y = 14 →
  29. 29.x + 6y = 21 and x + 3y = 15 →
  30. 30.8x + 3y = 79 and 3x + 8y = 64 →
  31. 31.8x + 7y = 1 and 7x + 8y = −1 →
  32. 32.2x + 7y = 60 and 7x + 2y = 75 →
  33. 33.x − 2y = −11 and x − 4y = −25 →
  34. 34.9x + 7y = 78 and 7x + 9y = 82 →
  35. 35.x + 6y = 38 and 6x + y = 53 →
  36. 36.x + 4y = 13 and 4x + y = −23 →
  37. 37.8x + 9y = 57 and 9x + 8y = 62 →
  38. 38.x − 2y = −11 and 4x − 3y = −19 →
  39. 39.x + 3y = 18 and 2x + 3y = 21 →
  40. 40.2x − 6y = −4 and x + y = 6 →

Answer key

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

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