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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 697 · 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 + 6y = 14 and 5x + 5y = 45 →
  2. 2.4x − 5y = −7 and 6x + 4y = 24 →
  3. 3.2x + 2y = −10 and 6x + 2y = 2 →
  4. 4.4x + 6y = 90 and 3x + y = 36 →
  5. 5.4x + 5y = 18 and 6x + 3y = 18 →
  6. 6.7x + y = 28 and x + 7y = 52 →
  7. 7.2x + 2y = 14 and 2x − y = 5 →
  8. 8.2x − 2y = −10 and x + y = −1 →
  9. 9.x + 7y = 57 and 7x + y = 63 →
  10. 10.x + 3y = −3 and x − 2y = −13 →
  11. 11.5x + 7y = 31 and 7x + 5y = 29 →
  12. 12.8x + 4y = 24 and 4x + 8y = 24 →
  13. 13.2x − y = −25 and 5x + 3y = −24 →
  14. 14.9x + 7y = −1 and 7x + 9y = −15 →
  15. 15.8x + 2y = 6 and 2x + 8y = −6 →
  16. 16.3x + 2y = −22 and 6x + 2y = −46 →
  17. 17.2x + 3y = −35 and 4x − y = −21 →
  18. 18.5x + 2y = 47 and 2x + 5y = 23 →
  19. 19.4x − 6y = 20 and 5x + y = −26 →
  20. 20.3x + 3y = 21 and 2x + y = 6 →
  21. 21.8x + 6y = −6 and 6x + 8y = −36 →
  22. 22.4x + y = 39 and 3x − 5y = 12 →
  23. 23.4x + 6y = 26 and 6x + 2y = 18 →
  24. 24.2x + 4y = 54 and 4x + 2y = 54 →
  25. 25.4x − y = −35 and 2x + 3y = −21 →
  26. 26.5x + 6y = −58 and 6x + 5y = −63 →
  27. 27.5x + 5y = −35 and 3x + 6y = −18 →
  28. 28.5x + 6y = 77 and 6x + 5y = 77 →
  29. 29.5x + 3y = −17 and 3x + 2y = −10 →
  30. 30.9x + 6y = 60 and 6x + 9y = 60 →
  31. 31.7x + 4y = −35 and 4x + 7y = −53 →
  32. 32.6x + 6y = 18 and x + 3y = 13 →
  33. 33.4x + 3y = −21 and 2x − y = −23 →
  34. 34.4x − y = −7 and 5x − 6y = −23 →
  35. 35.8x + 4y = 80 and 4x + 8y = 88 →
  36. 36.4x + y = 18 and 2x − 4y = 18 →
  37. 37.3x − 5y = −47 and 2x + 2y = −10 →
  38. 38.2x + 5y = 46 and 4x + 3y = 50 →
  39. 39.5x + 5y = 30 and 4x + 2y = 18 →
  40. 40.2x + 5y = 46 and x + 4y = 32 →

Answer key

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

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