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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 345 · 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. 1.6x + y = 7 and 4x + 3y = 7 →
  2. 2.3x + 4y = 0 and 2x − 2y = 14 →
  3. 3.3x + 9y = 99 and 9x + 3y = 81 →
  4. 4.2x + 3y = 19 and 2x − 5y = −53 →
  5. 5.2x + 2y = 26 and 3x + 5y = 55 →
  6. 6.x − 3y = −29 and 5x + 5y = −5 →
  7. 7.5x + 2y = 23 and 2x + 5y = 26 →
  8. 8.2x + 6y = 28 and 2x − 2y = −4 →
  9. 9.5x − 3y = 12 and 5x + 2y = −33 →
  10. 10.7x + 3y = 23 and 3x + 7y = −13 →
  11. 11.4x − 2y = −10 and 5x − 5y = −30 →
  12. 12.2x + 2y = 18 and 4x + 2y = 30 →
  13. 13.8x + 9y = 1 and 9x + 8y = 16 →
  14. 14.3x + 2y = 28 and 2x + 3y = 32 →
  15. 15.5x + 6y = −62 and 6x − 2y = −10 →
  16. 16.x − 4y = −20 and 5x + 4y = 68 →
  17. 17.6x + 4y = −38 and 4x + 6y = −22 →
  18. 18.4x + 3y = 42 and x + 5y = 19 →
  19. 19.7x + 9y = −15 and 9x + 7y = −1 →
  20. 20.5x − 4y = −18 and 6x − y = 5 →
  21. 21.3x + y = 32 and x + 3y = 32 →
  22. 22.4x − 6y = 70 and 5x − 4y = 63 →
  23. 23.3x + 2y = 7 and 4x + 6y = −14 →
  24. 24.x + y = −2 and 2x − 3y = 11 →
  25. 25.4x + 5y = 53 and 5x + 4y = 55 →
  26. 26.8x + 2y = −2 and 2x + 8y = 22 →
  27. 27.3x − 5y = −22 and 6x + 2y = −20 →
  28. 28.2x + 3y = −14 and 5x + 3y = −8 →
  29. 29.2x − 3y = 8 and 4x + 2y = 32 →
  30. 30.6x + 8y = 54 and 8x + 6y = 44 →
  31. 31.8x + 9y = −24 and 9x + 8y = −10 →
  32. 32.5x + 2y = 19 and 2x + 4y = 30 →
  33. 33.3x + 6y = −6 and x + 3y = −4 →
  34. 34.x + 5y = 29 and 6x − 2y = −18 →
  35. 35.4x + 3y = −1 and x − 5y = 17 →
  36. 36.x + 6y = 25 and 3x − 4y = 9 →
  37. 37.5x + 2y = 33 and 6x + y = 27 →
  38. 38.6x + y = 14 and x + 6y = 49 →
  39. 39.7x + 5y = 58 and 5x + 7y = 38 →
  40. 40.2x + 9y = 5 and 9x + 2y = −16 →

Answer key

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

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