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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 625 · 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 + 6y = 21 and 6x + 3y = −21 →
  2. 2.2x + 4y = 2 and 4x − 6y = −38 →
  3. 3.5x − 6y = 6 and x + y = −12 →
  4. 4.6x + 4y = 10 and 4x + 6y = −20 →
  5. 5.2x − 6y = 28 and 3x + 2y = −24 →
  6. 6.5x + 5y = −5 and 4x + 2y = 12 →
  7. 7.3x + 4y = 59 and x + 4y = 41 →
  8. 8.x + 2y = 4 and 4x + 5y = 7 →
  9. 9.x + 2y = −6 and 4x + 5y = −3 →
  10. 10.5x + y = 34 and x + 5y = 50 →
  11. 11.4x − y = 3 and 3x + y = 11 →
  12. 12.6x + 5y = 57 and 6x + 6y = 66 →
  13. 13.3x − 2y = 1 and 6x − 6y = −12 →
  14. 14.5x + y = −19 and x + 5y = 1 →
  15. 15.3x − y = −17 and x + 2y = −22 →
  16. 16.3x − 3y = 0 and 2x + 2y = 16 →
  17. 17.x − y = −4 and 3x + 2y = 18 →
  18. 18.3x − y = −8 and 3x − 5y = 8 →
  19. 19.2x + 8y = −40 and 8x + 2y = 20 →
  20. 20.4x + 7y = −13 and 7x + 4y = 2 →
  21. 21.3x − y = 4 and 3x + 4y = 14 →
  22. 22.3x + 3y = −3 and 5x − 6y = 61 →
  23. 23.6x + 4y = −16 and x − 6y = 44 →
  24. 24.6x + 3y = 60 and 5x − 4y = 37 →
  25. 25.8x + 2y = −64 and 2x + 8y = 14 →
  26. 26.2x − 3y = −16 and x + 6y = 37 →
  27. 27.6x + 6y = 72 and 6x + 2y = 56 →
  28. 28.4x − 4y = 0 and 4x + y = −10 →
  29. 29.5x − y = −46 and 4x − y = −38 →
  30. 30.3x + 6y = 30 and 3x − 2y = −2 →
  31. 31.6x − y = 32 and 2x + 5y = 32 →
  32. 32.9x + 8y = 81 and 8x + 9y = 89 →
  33. 33.6x + y = 33 and 2x + 4y = 22 →
  34. 34.6x + 8y = −72 and 8x + 6y = −82 →
  35. 35.4x + 3y = −27 and 3x + 4y = −15 →
  36. 36.5x + 6y = 13 and 3x + 2y = 11 →
  37. 37.8x + y = 13 and x + 8y = 41 →
  38. 38.3x − 4y = 40 and x + 4y = −24 →
  39. 39.x + 2y = 0 and 2x + y = 12 →
  40. 40.9x + 2y = 87 and 2x + 9y = 45 →

Answer key

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

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