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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 215 · 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 − y = 43 and 4x + y = 29 →
  2. 2.2x + 5y = 11 and 2x − 4y = −16 →
  3. 3.6x + 4y = 38 and 4x + y = 22 →
  4. 4.7x + y = 30 and x + 7y = 18 →
  5. 5.x + 4y = 0 and 4x + y = −15 →
  6. 6.x + 2y = −5 and 2x + y = −16 →
  7. 7.x + 2y = 1 and 4x − 6y = −66 →
  8. 8.6x + y = 26 and 2x + 2y = 12 →
  9. 9.4x − 6y = −36 and x + 2y = 19 →
  10. 10.x + 3y = 7 and 3x + y = −11 →
  11. 11.2x − 4y = −38 and x + 3y = 26 →
  12. 12.2x + 5y = −19 and 5x + 2y = 5 →
  13. 13.3x + 6y = 33 and 6x − y = 40 →
  14. 14.2x + 2y = −10 and 4x − 5y = −47 →
  15. 15.7x + 3y = −46 and 3x + 7y = −54 →
  16. 16.9x + 2y = 51 and 2x + 9y = 37 →
  17. 17.4x + 3y = −3 and 3x + 4y = −11 →
  18. 18.x + 9y = 79 and 9x + y = −9 →
  19. 19.2x − 2y = −18 and x + 3y = 7 →
  20. 20.3x + 6y = 54 and 4x + 5y = 57 →
  21. 21.4x + 6y = −48 and 5x + 5y = −45 →
  22. 22.3x + y = −18 and x + 5y = 22 →
  23. 23.x − 2y = −9 and 5x + y = 10 →
  24. 24.8x + 3y = 66 and 3x + 8y = 11 →
  25. 25.5x + y = 39 and x − 2y = −1 →
  26. 26.2x + 6y = 30 and 3x + y = −3 →
  27. 27.2x − 2y = 22 and 6x + 3y = 3 →
  28. 28.5x + 4y = −8 and x + 6y = −38 →
  29. 29.x + 5y = 30 and 5x − 6y = −5 →
  30. 30.x − 5y = −28 and 6x + y = −13 →
  31. 31.8x + 5y = 70 and 5x + 8y = 73 →
  32. 32.2x + 6y = 70 and 3x + y = 33 →
  33. 33.8x + 2y = 82 and 2x + 8y = 88 →
  34. 34.5x + y = −9 and x + 3y = 1 →
  35. 35.2x + 3y = −1 and 3x + 2y = 11 →
  36. 36.6x + 5y = 3 and 6x − 4y = −24 →
  37. 37.3x + 9y = 36 and 9x + 3y = 60 →
  38. 38.6x + y = 27 and x + 6y = −13 →
  39. 39.6x − 6y = 90 and 2x + 2y = −6 →
  40. 40.x − 3y = −8 and 4x − 6y = −14 →

Answer key

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

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