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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 241 · 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. 1.2x + 4y = 2 and 4x + 2y = 22 →
  2. 2.2x + y = 6 and x + 2y = −6 →
  3. 3.6x + 5y = 25 and 2x + 4y = 6 →
  4. 4.3x + 8y = 82 and 8x + 3y = 72 →
  5. 5.4x + y = −24 and x + 4y = 24 →
  6. 6.6x + 8y = 36 and 8x + 6y = 34 →
  7. 7.2x + 9y = 23 and 9x + 2y = 65 →
  8. 8.6x + 3y = 0 and 4x + 5y = −6 →
  9. 9.x + 2y = 15 and 3x − y = 24 →
  10. 10.5x + 2y = 32 and 5x − 3y = 2 →
  11. 11.7x + 6y = 84 and 6x + 7y = 85 →
  12. 12.5x + 2y = 32 and 4x − 5y = 19 →
  13. 13.x + 5y = 43 and 3x − y = 1 →
  14. 14.4x + 3y = 12 and x + 5y = 37 →
  15. 15.3x + 3y = 6 and 6x + 3y = 9 →
  16. 16.3x + 6y = −15 and 6x − 2y = 26 →
  17. 17.5x + 2y = 17 and 4x − 6y = 82 →
  18. 18.4x + 2y = 46 and x − 5y = −38 →
  19. 19.4x + 8y = −40 and 8x + 4y = −56 →
  20. 20.4x + 6y = −12 and 3x − 4y = 59 →
  21. 21.6x + 5y = 32 and 5x + 6y = 34 →
  22. 22.x − 6y = −24 and 5x + 2y = 40 →
  23. 23.x + 3y = 10 and 5x + 5y = 30 →
  24. 24.3x + 6y = −63 and x + y = −13 →
  25. 25.3x + 6y = 45 and x − 4y = −33 →
  26. 26.6x + 9y = 78 and 9x + 6y = 72 →
  27. 27.5x − 3y = 44 and 5x + 6y = −28 →
  28. 28.3x + 2y = 10 and 4x − 2y = 4 →
  29. 29.8x + 4y = 20 and 4x + 8y = −8 →
  30. 30.3x + 3y = −24 and 3x + 4y = −33 →
  31. 31.8x + 3y = −85 and 3x + 8y = −80 →
  32. 32.6x + 3y = 6 and 4x + y = 10 →
  33. 33.6x − 4y = −10 and 3x + 5y = 44 →
  34. 34.4x + y = −22 and 5x + 5y = −5 →
  35. 35.4x − 4y = −24 and x + 4y = 34 →
  36. 36.3x − 2y = −37 and 2x − 3y = −33 →
  37. 37.x − 3y = −31 and 6x + 5y = −2 →
  38. 38.6x + 2y = −40 and 5x − 6y = −87 →
  39. 39.8x + 6y = −24 and 6x + 8y = −46 →
  40. 40.4x − 2y = 6 and 2x − 2y = −4 →

Answer key

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

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