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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 107 · 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 + 2y = 28 and 2x − 6y = −18 →
  2. 2.5x + 8y = 102 and 8x + 5y = 93 →
  3. 3.5x + 4y = 7 and x − 5y = −16 →
  4. 4.x + 7y = 19 and 7x + y = −11 →
  5. 5.3x + y = 1 and 6x − 4y = 50 →
  6. 6.4x − 5y = −7 and 2x + 2y = 10 →
  7. 7.5x − 2y = −46 and x − 2y = −14 →
  8. 8.5x + 4y = 46 and 4x + 5y = 53 →
  9. 9.x + y = −7 and 6x + 3y = −45 →
  10. 10.3x − 6y = −18 and 5x + 2y = 42 →
  11. 11.6x + y = 39 and x + 2y = 12 →
  12. 12.2x + 4y = −14 and 6x − 5y = 60 →
  13. 13.3x + 5y = −32 and 6x − 6y = 48 →
  14. 14.3x + 8y = 78 and 8x + 3y = 43 →
  15. 15.6x + 3y = −9 and 4x + 5y = 3 →
  16. 16.6x + y = 30 and x − 5y = −26 →
  17. 17.3x + 4y = 32 and 4x + 2y = 36 →
  18. 18.4x + 3y = 11 and 6x − 2y = 10 →
  19. 19.3x − y = −4 and 5x + 4y = 33 →
  20. 20.x + 6y = 24 and 6x + y = −31 →
  21. 21.2x + 5y = 11 and 6x + y = 19 →
  22. 22.x − 6y = −52 and 3x − 3y = −21 →
  23. 23.2x + 3y = 21 and 5x − 2y = 43 →
  24. 24.2x − 4y = 20 and 5x − 3y = 43 →
  25. 25.4x + 3y = 32 and 3x + 6y = 54 →
  26. 26.2x + 8y = −8 and 8x + 2y = 28 →
  27. 27.2x + 5y = 14 and 2x + 6y = 16 →
  28. 28.x + 2y = 1 and 3x − 4y = −47 →
  29. 29.x + 3y = 4 and 3x + y = −12 →
  30. 30.3x + 4y = 17 and 4x − 5y = −29 →
  31. 31.4x + 2y = −8 and 6x + y = −28 →
  32. 32.3x − 6y = −63 and 3x − 2y = −35 →
  33. 33.x − 3y = −13 and 3x − 4y = −4 →
  34. 34.6x + 7y = −1 and 7x + 6y = 1 →
  35. 35.4x + 6y = 48 and 6x + 4y = 42 →
  36. 36.3x + y = −15 and x + 3y = 19 →
  37. 37.5x + 6y = −14 and 6x + 5y = −8 →
  38. 38.9x + 5y = −42 and 5x + 9y = 14 →
  39. 39.2x + 2y = 22 and 6x + 5y = 57 →
  40. 40.7x + 3y = 38 and 3x + 7y = 62 →

Answer key

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

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