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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 189 · 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 − 2y = −20 and 2x + 2y = 4 →
  2. 2.4x + 5y = 34 and x + 3y = 12 →
  3. 3.5x + 5y = 50 and x − 5y = 4 →
  4. 4.2x + 9y = 74 and 9x + 2y = 25 →
  5. 5.3x + 5y = 18 and 4x + 6y = 22 →
  6. 6.5x + y = 37 and 5x + 5y = 45 →
  7. 7.5x + 4y = −26 and 6x + 4y = −24 →
  8. 8.5x + 5y = −35 and 6x + 2y = −18 →
  9. 9.5x − 3y = 35 and 5x + 6y = −10 →
  10. 10.3x + 2y = 26 and 2x − 3y = 13 →
  11. 11.4x − 2y = −28 and 4x − 5y = −46 →
  12. 12.3x + 5y = −32 and x + y = −6 →
  13. 13.6x − 4y = −62 and 5x + 2y = −9 →
  14. 14.6x + 2y = 40 and 4x − y = 29 →
  15. 15.2x − 5y = −3 and x + 4y = 5 →
  16. 16.4x + y = 15 and 2x + 5y = 21 →
  17. 17.x − 5y = −31 and 3x − y = −23 →
  18. 18.7x + 2y = 59 and 2x + 7y = 49 →
  19. 19.5x + 6y = 52 and 6x + 5y = 58 →
  20. 20.3x − y = 2 and 5x + 6y = 57 →
  21. 21.3x + 7y = −46 and 7x + 3y = −54 →
  22. 22.3x − 6y = −27 and 6x + 2y = 16 →
  23. 23.4x − y = 31 and 6x + 5y = 53 →
  24. 24.4x + 5y = 31 and 5x + 4y = 41 →
  25. 25.9x + 2y = 74 and 2x + 9y = 25 →
  26. 26.2x + 8y = −34 and 8x + 2y = −76 →
  27. 27.2x − y = 9 and 2x + 5y = 51 →
  28. 28.5x + 5y = 20 and 3x + 5y = 16 →
  29. 29.2x + y = −5 and 2x − 6y = −54 →
  30. 30.9x + 3y = 69 and 3x + 9y = 87 →
  31. 31.7x + 5y = 16 and 5x + 7y = 32 →
  32. 32.4x + 3y = 14 and 2x + 2y = 4 →
  33. 33.5x + 4y = 34 and 2x + 2y = 14 →
  34. 34.6x − 2y = −50 and x − 2y = −20 →
  35. 35.3x + 5y = 58 and 5x + 3y = 54 →
  36. 36.2x + 3y = 36 and 3x + 2y = 39 →
  37. 37.6x + 7y = 69 and 7x + 6y = 74 →
  38. 38.5x + 6y = 17 and 6x + 5y = 16 →
  39. 39.5x + 4y = 17 and x + 2y = −5 →
  40. 40.x + 3y = 6 and 4x − y = 11 →

Answer key

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

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