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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 623 · 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 + 5y = 64 and 6x − y = 16 →
  2. 2.6x + 3y = 72 and 3x + 6y = 63 →
  3. 3.4x + 5y = 23 and 2x + 4y = 22 →
  4. 4.5x + y = −35 and x + 5y = 17 →
  5. 5.7x + 3y = 0 and 3x + 7y = −40 →
  6. 6.9x + 2y = 16 and 2x + 9y = −5 →
  7. 7.7x + 8y = 0 and 8x + 7y = −15 →
  8. 8.5x + 9y = −11 and 9x + 5y = −31 →
  9. 9.x + 6y = 39 and x + 3y = 21 →
  10. 10.9x + 4y = 60 and 4x + 9y = 70 →
  11. 11.3x + 2y = 11 and 2x + 4y = 26 →
  12. 12.x − 3y = −16 and x − y = −2 →
  13. 13.6x + 4y = −22 and 4x + 6y = −38 →
  14. 14.4x + y = −15 and 6x + 6y = 0 →
  15. 15.7x + 5y = −74 and 5x + 7y = −70 →
  16. 16.4x + 2y = −4 and x + 2y = −10 →
  17. 17.5x − 2y = 4 and 6x + 4y = −40 →
  18. 18.x − 5y = −33 and 2x − 6y = −42 →
  19. 19.9x + 3y = 72 and 3x + 9y = 48 →
  20. 20.4x + 3y = 39 and 3x + 4y = 45 →
  21. 21.3x + 6y = 66 and 5x + 2y = 38 →
  22. 22.4x + 5y = 34 and x + 5y = 16 →
  23. 23.x + 5y = 39 and 5x + y = 27 →
  24. 24.x − 2y = 2 and x + 3y = −23 →
  25. 25.3x + y = 23 and x + 6y = 53 →
  26. 26.2x + 2y = −16 and 5x − 2y = 9 →
  27. 27.4x + 2y = −28 and 2x + 4y = −32 →
  28. 28.7x + 5y = −69 and 5x + 7y = −63 →
  29. 29.4x + 6y = 16 and 6x + 4y = 14 →
  30. 30.5x + y = −25 and 5x + 3y = −15 →
  31. 31.6x + 2y = −50 and 6x − y = −56 →
  32. 32.4x + 8y = −12 and 8x + 4y = 0 →
  33. 33.6x + 3y = 39 and 6x + 6y = 36 →
  34. 34.3x − 3y = 48 and 6x + 5y = 19 →
  35. 35.3x + y = −26 and 4x + 6y = −44 →
  36. 36.3x + 2y = 21 and x − 5y = −44 →
  37. 37.2x + 5y = −31 and 5x + 3y = −30 →
  38. 38.5x + 6y = −69 and 6x + 5y = −63 →
  39. 39.4x + 5y = 10 and x + 4y = −3 →
  40. 40.5x + y = 21 and 6x + 3y = 18 →

Answer key

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

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