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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 824 · 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 + 5y = 8 and 5x − y = 4 →
  2. 2.9x + 4y = −90 and 4x + 9y = −105 →
  3. 3.4x + 2y = 0 and 2x + 4y = −12 →
  4. 4.x − y = 0 and 2x − 3y = 2 →
  5. 5.5x + 5y = −5 and 5x + 2y = 13 →
  6. 6.5x + 6y = 62 and 6x + 5y = 59 →
  7. 7.4x + 3y = 26 and 3x + 4y = 30 →
  8. 8.3x − 3y = −27 and 6x + 2y = 10 →
  9. 9.5x + 4y = 28 and 4x + 3y = 22 →
  10. 10.6x − 2y = 28 and 2x + 2y = 20 →
  11. 11.2x − y = −6 and x + y = 9 →
  12. 12.6x + 9y = −24 and 9x + 6y = −51 →
  13. 13.3x − 5y = −16 and 2x + 5y = −19 →
  14. 14.2x + 4y = −16 and 4x + 2y = 4 →
  15. 15.6x + 4y = 14 and 2x − 4y = −6 →
  16. 16.6x + 8y = 58 and 8x + 6y = 54 →
  17. 17.2x + 4y = 24 and 4x + 2y = 30 →
  18. 18.6x + 5y = −42 and 5x + 6y = −46 →
  19. 19.6x + 9y = 15 and 9x + 6y = 15 →
  20. 20.x + y = −2 and 4x − 2y = 10 →
  21. 21.6x + 8y = 10 and 8x + 6y = 18 →
  22. 22.4x − y = −23 and x − y = −8 →
  23. 23.x + 6y = 43 and 2x + 5y = 30 →
  24. 24.5x + 3y = −22 and 3x − 4y = 10 →
  25. 25.9x + 4y = 7 and 4x + 9y = 32 →
  26. 26.4x + y = −15 and 6x − 5y = −81 →
  27. 27.4x − 3y = 51 and 2x + y = 13 →
  28. 28.3x − y = −28 and 3x + y = −26 →
  29. 29.2x + 8y = 26 and 8x + 2y = −46 →
  30. 30.6x + 4y = −62 and 4x + 6y = −48 →
  31. 31.x + 2y = 2 and 6x + 2y = −18 →
  32. 32.2x + y = 5 and 4x + 3y = 19 →
  33. 33.8x + 4y = −56 and 4x + 8y = −4 →
  34. 34.x − 3y = 13 and 2x + y = −23 →
  35. 35.2x − 4y = 6 and 2x − 5y = 5 →
  36. 36.5x + 5y = 5 and 5x + 6y = 9 →
  37. 37.x + 4y = −19 and 3x + 6y = −15 →
  38. 38.4x + 5y = 55 and x + 2y = 19 →
  39. 39.2x − 4y = −46 and 6x − 2y = −58 →
  40. 40.2x + 9y = −56 and 9x + 2y = 56 →

Answer key

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

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