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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 870 · 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 + 3y = 10 and 3x + 2y = 5 →
  2. 2.4x + y = 5 and 5x + 3y = 8 →
  3. 3.3x + 6y = 24 and 6x + 3y = 39 →
  4. 4.2x + 3y = 21 and x + 5y = 14 →
  5. 5.4x − 6y = −20 and x − 6y = −41 →
  6. 6.3x + 2y = 11 and 2x + 3y = −1 →
  7. 7.2x − 6y = −54 and x + 5y = 29 →
  8. 8.x + 4y = 31 and 4x + y = 19 →
  9. 9.6x + y = 0 and x + 6y = −35 →
  10. 10.x + 4y = −22 and x + 3y = −15 →
  11. 11.5x + 5y = −15 and 5x + 4y = −6 →
  12. 12.x + 6y = −4 and 2x + 4y = 8 →
  13. 13.4x + 3y = 33 and 3x + 4y = 30 →
  14. 14.3x + 5y = 4 and 5x + 4y = 11 →
  15. 15.2x + 3y = 3 and 3x + 4y = 6 →
  16. 16.5x + 4y = −17 and 3x − y = −34 →
  17. 17.3x + 4y = 16 and 4x + 3y = 26 →
  18. 18.6x + 6y = 84 and x + 2y = 21 →
  19. 19.3x + 4y = −5 and 4x + 3y = −2 →
  20. 20.x − 2y = −12 and 4x − 4y = −32 →
  21. 21.5x − 6y = −1 and 4x + 4y = 8 →
  22. 22.x + 5y = −29 and 4x − y = 31 →
  23. 23.2x + 2y = 24 and 2x + 3y = 31 →
  24. 24.9x + y = −25 and x + 9y = 15 →
  25. 25.2x + 8y = −50 and 8x + 2y = 40 →
  26. 26.4x + y = −4 and x + 4y = −31 →
  27. 27.6x + 2y = 22 and 2x + 6y = 50 →
  28. 28.5x + 6y = 23 and 2x − 2y = −26 →
  29. 29.x + 5y = 41 and 6x + y = 14 →
  30. 30.9x + 2y = 11 and 2x + 9y = 11 →
  31. 31.2x − 4y = −8 and x + 6y = 44 →
  32. 32.6x + y = 55 and 3x + y = 28 →
  33. 33.x + y = −12 and 4x − 4y = 16 →
  34. 34.5x + 6y = 1 and 2x + 2y = −2 →
  35. 35.3x + y = 14 and x + 3y = −14 →
  36. 36.5x − 3y = 13 and 6x + 2y = 10 →
  37. 37.3x − 2y = −13 and 4x + 4y = 36 →
  38. 38.3x + y = 33 and 4x − 4y = 12 →
  39. 39.6x + 8y = 6 and 8x + 6y = 36 →
  40. 40.8x + 3y = 37 and 3x + 8y = −48 →

Answer key

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

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