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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 562 · 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. 1.2x + 4y = 40 and 4x + 2y = 38 →
  2. 2.5x − 3y = 34 and x − y = 10 →
  3. 3.2x + 8y = 34 and 8x + 2y = 16 →
  4. 4.7x + 4y = −9 and 4x + 7y = 9 →
  5. 5.2x − 5y = −31 and 2x − 2y = −22 →
  6. 6.3x + 4y = 20 and 5x + y = 39 →
  7. 7.9x + y = 73 and x + 9y = −63 →
  8. 8.x − 2y = −15 and 2x + y = 15 →
  9. 9.2x − 6y = −2 and 6x + 4y = 16 →
  10. 10.3x + 2y = 30 and 6x + 2y = 42 →
  11. 11.3x + 2y = 9 and 3x + 5y = 18 →
  12. 12.3x + 3y = 27 and 3x + 6y = 51 →
  13. 13.4x + 5y = −2 and 3x − 5y = −54 →
  14. 14.x − 3y = −25 and x − y = −7 →
  15. 15.4x − 3y = 9 and 3x + 4y = 63 →
  16. 16.x − 5y = −3 and 5x + 4y = 14 →
  17. 17.2x + 4y = 14 and x + 6y = 15 →
  18. 18.7x + 5y = 6 and 5x + 7y = −6 →
  19. 19.7x + 4y = 25 and 4x + 7y = 19 →
  20. 20.4x − 3y = −18 and x − y = −5 →
  21. 21.6x + 2y = 20 and x − 5y = −2 →
  22. 22.x + 3y = 22 and 3x + y = 10 →
  23. 23.x − 2y = 12 and x − 6y = 32 →
  24. 24.3x − y = 14 and 2x + y = 16 →
  25. 25.4x + 6y = 58 and 2x + 2y = 20 →
  26. 26.5x + 6y = 69 and 6x + 5y = 63 →
  27. 27.5x − y = 6 and x + 3y = 14 →
  28. 28.7x + y = 30 and x + 7y = −30 →
  29. 29.4x + 6y = 30 and 4x + 4y = 12 →
  30. 30.6x + 4y = 44 and 4x + 6y = 56 →
  31. 31.x + 6y = 49 and 5x + 2y = 49 →
  32. 32.4x + 2y = 14 and 2x + 4y = −20 →
  33. 33.5x + 4y = 18 and 4x + 5y = 9 →
  34. 34.6x − 5y = −15 and 6x + y = 39 →
  35. 35.6x − 5y = 4 and 2x − 6y = −16 →
  36. 36.3x + 2y = −26 and 2x + 3y = −24 →
  37. 37.3x − 3y = 48 and 2x + 3y = −8 →
  38. 38.5x + 6y = 1 and 6x + 5y = 10 →
  39. 39.3x + 4y = −7 and 4x + 3y = −14 →
  40. 40.3x − y = 4 and 3x + 5y = 16 →

Answer key

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

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