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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 292 · 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 + 7y = 13 and 7x + 2y = 23 →
  2. 2.4x + 2y = −2 and 2x + 4y = 8 →
  3. 3.2x + 7y = 25 and 7x + 2y = 20 →
  4. 4.5x + 6y = 35 and 6x + 5y = 31 →
  5. 5.3x + 2y = 30 and 2x + 3y = 35 →
  6. 6.2x + y = 10 and x + 2y = −4 →
  7. 7.4x + 9y = −48 and 9x + 4y = −43 →
  8. 8.9x + 6y = −12 and 6x + 9y = −3 →
  9. 9.5x − y = −32 and 3x − y = −18 →
  10. 10.x + y = 14 and 3x + 5y = 56 →
  11. 11.3x + 5y = −12 and 5x + 3y = 12 →
  12. 12.7x + 4y = 48 and 4x + 7y = 51 →
  13. 13.4x − 5y = −7 and 4x + 2y = 42 →
  14. 14.x + 6y = 8 and 6x + y = 13 →
  15. 15.x + 3y = −4 and 2x − 3y = 10 →
  16. 16.3x + 6y = 66 and 5x + 4y = 62 →
  17. 17.3x + 2y = 22 and 2x + 3y = 18 →
  18. 18.2x + 5y = 59 and 4x + 4y = 64 →
  19. 19.6x + 2y = −26 and 3x + 6y = 12 →
  20. 20.5x + 3y = −24 and 2x − 2y = 0 →
  21. 21.5x + 3y = −6 and 5x − 2y = 29 →
  22. 22.9x + 4y = 42 and 4x + 9y = 62 →
  23. 23.2x + 5y = 34 and 5x + 2y = 22 →
  24. 24.3x − 3y = 9 and 2x + y = 9 →
  25. 25.3x + y = −16 and 3x + 5y = −32 →
  26. 26.4x + y = 18 and 3x + 5y = 22 →
  27. 27.2x + y = 10 and 2x − 2y = −8 →
  28. 28.7x + 2y = 8 and 2x + 7y = −17 →
  29. 29.5x + 3y = −59 and 2x + 2y = −30 →
  30. 30.5x − y = 33 and x − y = 5 →
  31. 31.5x − 5y = 80 and 3x + y = 16 →
  32. 32.2x + 7y = 27 and 7x + 2y = −18 →
  33. 33.3x + 6y = −18 and 2x − y = 13 →
  34. 34.4x + 2y = 30 and x + y = 7 →
  35. 35.6x + 6y = 96 and 5x + 2y = 56 →
  36. 36.3x + 7y = −70 and 7x + 3y = −70 →
  37. 37.4x − 4y = 28 and 3x − 2y = 20 →
  38. 38.6x + 4y = 50 and x − y = −5 →
  39. 39.5x − 2y = 23 and 4x + 6y = 26 →
  40. 40.5x + 6y = 33 and 4x + y = 15 →

Answer key

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

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