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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 676 · 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.x + 3y = 26 and x + 2y = 18 →
  2. 2.5x + 5y = −25 and 3x + 2y = −14 →
  3. 3.5x + y = −40 and x + 5y = −32 →
  4. 4.3x + 6y = 69 and 5x + 2y = 59 →
  5. 5.x + 4y = 13 and 2x + 5y = 17 →
  6. 6.3x + 2y = 15 and 6x + y = 39 →
  7. 7.2x + 6y = −12 and x + y = −8 →
  8. 8.4x + y = −11 and 2x − 4y = −10 →
  9. 9.x + 5y = 14 and 3x + 3y = 6 →
  10. 10.5x + 7y = −58 and 7x + 5y = −38 →
  11. 11.x + 5y = 41 and 3x − 2y = −30 →
  12. 12.x + 4y = 3 and 3x − 6y = −45 →
  13. 13.4x + 4y = −12 and x − 4y = 2 →
  14. 14.5x − 6y = −3 and 5x + 4y = 27 →
  15. 15.4x − 5y = 3 and 4x − 3y = 5 →
  16. 16.x − y = 13 and 2x + 3y = −14 →
  17. 17.5x − y = 23 and 4x − 3y = 25 →
  18. 18.2x + 3y = −5 and 5x + 5y = −20 →
  19. 19.3x + y = −19 and 5x + y = −37 →
  20. 20.3x + 6y = −63 and 6x + 3y = −45 →
  21. 21.5x + 4y = 39 and x − 3y = −15 →
  22. 22.x − y = 4 and 6x + 6y = 84 →
  23. 23.2x + 4y = 28 and 4x − 2y = −4 →
  24. 24.2x + 2y = 20 and 6x + y = 50 →
  25. 25.2x − 6y = 12 and 6x + 3y = 15 →
  26. 26.2x + 4y = 12 and 6x − y = 23 →
  27. 27.8x + 4y = 44 and 4x + 8y = 76 →
  28. 28.3x + 9y = 54 and 9x + 3y = 90 →
  29. 29.6x + y = 43 and 3x + 5y = 26 →
  30. 30.x + 2y = −6 and 4x + y = −31 →
  31. 31.x − 5y = 9 and 4x + 2y = −30 →
  32. 32.x + 2y = 9 and 2x + y = 15 →
  33. 33.x − 6y = −23 and 6x + y = 10 →
  34. 34.9x + 7y = −23 and 7x + 9y = 7 →
  35. 35.6x + 2y = −54 and 6x + y = −48 →
  36. 36.x − 2y = −7 and 2x + 2y = 16 →
  37. 37.4x − 5y = −8 and 5x + 5y = 35 →
  38. 38.2x − y = 15 and 6x + 4y = 66 →
  39. 39.3x − 6y = 15 and 6x + 5y = 64 →
  40. 40.4x + y = 14 and 6x − 2y = 0 →

Answer key

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

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