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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 765 · 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. 1.3x + y = 15 and x + 3y = 29 →
  2. 2.8x + 7y = −43 and 7x + 8y = −32 →
  3. 3.9x + y = 33 and x + 9y = −23 →
  4. 4.x + 7y = 26 and 7x + y = −58 →
  5. 5.4x + 6y = −40 and 6x − 4y = 18 →
  6. 6.9x + 2y = −49 and 2x + 9y = 49 →
  7. 7.5x + 6y = 47 and 2x + y = 9 →
  8. 8.4x + y = 24 and 3x + 3y = 36 →
  9. 9.8x + 5y = 62 and 5x + 8y = 29 →
  10. 10.2x + 4y = 34 and 4x − 4y = 20 →
  11. 11.x + 3y = 18 and 5x − y = 10 →
  12. 12.6x + 5y = −1 and 6x + 6y = −6 →
  13. 13.8x + y = −59 and x + 8y = 32 →
  14. 14.6x − 6y = 18 and 5x + 3y = −57 →
  15. 15.5x − 6y = 10 and 2x + 2y = −18 →
  16. 16.2x + 4y = 12 and 2x − 2y = −12 →
  17. 17.6x + 5y = −57 and 2x + 3y = −31 →
  18. 18.x + 4y = 37 and 4x + y = 43 →
  19. 19.3x + y = 15 and x + 3y = −3 →
  20. 20.3x + 5y = 34 and 2x − 6y = −24 →
  21. 21.5x + 5y = 60 and 5x + 2y = 48 →
  22. 22.3x − 5y = 25 and 6x + 4y = 22 →
  23. 23.3x − 2y = 24 and 4x + 3y = 15 →
  24. 24.x + 6y = −32 and 4x + 6y = −20 →
  25. 25.5x + 2y = −48 and 4x + y = −36 →
  26. 26.8x + 7y = −43 and 7x + 8y = −32 →
  27. 27.4x + 3y = 30 and 3x + 4y = 33 →
  28. 28.x + 7y = 22 and 7x + y = 58 →
  29. 29.5x + 3y = −24 and 5x + y = −18 →
  30. 30.5x + 6y = −42 and 6x + 5y = −46 →
  31. 31.4x − 2y = 28 and 2x + 5y = 2 →
  32. 32.5x + y = 28 and x + 5y = 20 →
  33. 33.2x − 2y = 28 and 2x + y = 13 →
  34. 34.3x + y = −20 and 2x + 4y = −10 →
  35. 35.5x + y = 15 and 4x + 6y = 38 →
  36. 36.5x + 4y = −10 and 5x − 6y = −60 →
  37. 37.5x + 4y = −9 and x + 5y = 15 →
  38. 38.4x − 5y = 4 and 5x − 6y = 6 →
  39. 39.9x + 6y = 99 and 6x + 9y = 111 →
  40. 40.3x − 2y = −29 and 6x − 5y = −62 →

Answer key

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

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