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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 156 · 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. 1.4x + 5y = 6 and 5x − 2y = −9 →
  2. 2.6x − 4y = 30 and 6x − 3y = 27 →
  3. 3.5x + 3y = 61 and 6x + y = 55 →
  4. 4.9x + 6y = 84 and 6x + 9y = 96 →
  5. 5.x + y = −16 and 4x − 6y = 26 →
  6. 6.3x − 2y = −17 and 5x + 5y = −45 →
  7. 7.x + y = 4 and 6x + 2y = 36 →
  8. 8.5x + 2y = 34 and 2x + 5y = 1 →
  9. 9.2x + 4y = 36 and 5x − y = 2 →
  10. 10.x + y = 4 and 4x + 5y = 24 →
  11. 11.3x − 5y = 9 and 2x − 5y = 16 →
  12. 12.2x + 7y = −29 and 7x + 2y = 11 →
  13. 13.7x + 2y = 20 and 2x + 7y = 25 →
  14. 14.6x + 3y = 18 and 5x − y = 1 →
  15. 15.4x + 3y = 41 and x − 2y = −9 →
  16. 16.8x + 3y = 0 and 3x + 8y = −55 →
  17. 17.5x + 3y = 39 and x + y = 11 →
  18. 18.5x + y = −41 and 6x + 5y = −34 →
  19. 19.4x − 4y = −24 and x + 4y = 39 →
  20. 20.x + y = −12 and x − 5y = 12 →
  21. 21.3x + 4y = 39 and 4x + 3y = 31 →
  22. 22.2x + 3y = −22 and x − 2y = 3 →
  23. 23.3x + y = 31 and x + 3y = 29 →
  24. 24.8x + 7y = −48 and 7x + 8y = −57 →
  25. 25.5x + y = 12 and x + 4y = 29 →
  26. 26.2x − 6y = 54 and 6x + 6y = −30 →
  27. 27.x + 5y = 17 and x + 3y = 7 →
  28. 28.4x + 5y = 37 and 2x + 4y = 20 →
  29. 29.2x + y = 12 and x + 2y = −3 →
  30. 30.x + y = 11 and 2x − 6y = −2 →
  31. 31.3x + y = 15 and x + 3y = 29 →
  32. 32.4x − 6y = 6 and x + y = 4 →
  33. 33.4x − 5y = −56 and 6x + 2y = −46 →
  34. 34.3x + y = 0 and 6x + 3y = 3 →
  35. 35.6x − 3y = 3 and x + 2y = 3 →
  36. 36.5x + 7y = −28 and 7x + 5y = 4 →
  37. 37.6x + 4y = 70 and 2x + 2y = 26 →
  38. 38.x − 2y = −11 and x + 3y = 29 →
  39. 39.4x + 3y = −14 and 3x + 4y = −21 →
  40. 40.4x + 3y = −49 and 3x + 4y = −49 →

Answer key

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

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