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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 285 · 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.x + 3y = 10 and 3x + y = 14 →
  2. 2.9x + 8y = −66 and 8x + 9y = −70 →
  3. 3.2x − 2y = −10 and 3x + 4y = 34 →
  4. 4.6x − y = −47 and 4x − y = −31 →
  5. 5.3x + 4y = 33 and 6x + 4y = 54 →
  6. 6.2x − 5y = 3 and 3x + y = 30 →
  7. 7.2x − 6y = −46 and 3x + y = 11 →
  8. 8.2x + 6y = −28 and 6x + 2y = −4 →
  9. 9.x + 6y = 51 and x − 2y = −5 →
  10. 10.6x + 8y = 104 and 8x + 6y = 106 →
  11. 11.2x + 4y = 16 and 4x + 2y = 2 →
  12. 12.6x + 6y = 48 and x − 5y = 2 →
  13. 13.4x + 4y = −20 and 2x − 4y = −4 →
  14. 14.7x + 6y = −13 and 6x + 7y = 0 →
  15. 15.6x + y = −15 and 5x − 6y = −74 →
  16. 16.5x − y = 48 and 2x − 6y = 36 →
  17. 17.6x − 2y = 40 and 6x − 4y = 26 →
  18. 18.5x + y = 11 and x + 5y = 31 →
  19. 19.8x + 9y = 120 and 9x + 8y = 118 →
  20. 20.2x − 5y = −13 and 4x − 6y = −22 →
  21. 21.5x + 6y = 57 and 2x − 3y = −15 →
  22. 22.6x + y = 3 and x + 6y = −52 →
  23. 23.4x + 4y = 0 and 4x − 4y = 72 →
  24. 24.3x − 3y = 9 and x + 3y = 27 →
  25. 25.7x + 8y = 57 and 8x + 7y = 63 →
  26. 26.4x − 5y = 28 and 2x + 2y = −4 →
  27. 27.5x + 7y = 56 and 7x + 5y = 64 →
  28. 28.6x + 2y = −24 and 2x − 6y = 52 →
  29. 29.5x + 8y = 18 and 8x + 5y = −18 →
  30. 30.4x − 2y = −20 and 6x − 2y = −28 →
  31. 31.7x + 6y = −23 and 6x + 7y = −16 →
  32. 32.x + 2y = 2 and 2x + y = 13 →
  33. 33.2x + 9y = 58 and 9x + 2y = −47 →
  34. 34.6x − 3y = −6 and 3x + y = 17 →
  35. 35.5x + y = −24 and x + 5y = 24 →
  36. 36.4x − 4y = 48 and 2x + 6y = −8 →
  37. 37.3x − 3y = −45 and 6x − 2y = −66 →
  38. 38.4x + y = 7 and 3x − 6y = 66 →
  39. 39.9x + 6y = 30 and 6x + 9y = 30 →
  40. 40.5x − 3y = −12 and x + 4y = 39 →

Answer key

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

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