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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 242 · 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 = 0 and 5x − 3y = 33 →
  2. 2.9x + y = 56 and x + 9y = 24 →
  3. 3.3x − 2y = −9 and x + 3y = 30 →
  4. 4.9x + 6y = −51 and 6x + 9y = −69 →
  5. 5.3x + 9y = 60 and 9x + 3y = 84 →
  6. 6.x + 3y = 22 and x − 6y = −23 →
  7. 7.5x + 7y = 27 and 7x + 5y = 33 →
  8. 8.4x − 2y = −2 and 2x − 4y = −10 →
  9. 9.3x + y = 4 and 5x + 4y = 2 →
  10. 10.4x + 3y = 50 and 3x + 4y = 48 →
  11. 11.6x + y = −41 and 2x + 6y = 26 →
  12. 12.4x + 6y = 40 and 5x + 4y = 22 →
  13. 13.5x − 2y = 13 and 4x − 6y = 6 →
  14. 14.6x − 2y = 28 and 5x − 6y = 6 →
  15. 15.x + y = 13 and 3x + 2y = 31 →
  16. 16.3x + y = 22 and x + 3y = −6 →
  17. 17.6x + 4y = 14 and x + 2y = −7 →
  18. 18.x + 4y = −16 and 4x + y = 26 →
  19. 19.9x + 3y = 21 and 3x + 9y = 39 →
  20. 20.5x + 3y = 46 and x + 5y = 40 →
  21. 21.x + 6y = 43 and x + 4y = 31 →
  22. 22.5x + y = 20 and 4x + 6y = 42 →
  23. 23.4x + y = 30 and x + 4y = 30 →
  24. 24.6x − 3y = 36 and 5x + 6y = −4 →
  25. 25.x + 4y = 33 and 4x + y = 27 →
  26. 26.4x − 6y = −64 and 6x − 3y = −60 →
  27. 27.4x + 2y = 36 and 6x + 4y = 62 →
  28. 28.4x + 6y = −6 and 6x + 4y = 6 →
  29. 29.6x + 4y = 48 and 3x − y = 6 →
  30. 30.6x + 8y = 30 and 8x + 6y = 54 →
  31. 31.4x + y = 12 and 6x − y = 8 →
  32. 32.8x + 4y = 16 and 4x + 8y = −40 →
  33. 33.6x − 2y = −34 and x + 3y = 1 →
  34. 34.x − 6y = 31 and 2x + 6y = −28 →
  35. 35.7x + 2y = −43 and 2x + 7y = 7 →
  36. 36.4x − 6y = −6 and x + 4y = 15 →
  37. 37.5x + 6y = 6 and 4x + 2y = −12 →
  38. 38.5x + 2y = 17 and 3x + 2y = 3 →
  39. 39.x + 6y = 17 and 6x + y = −3 →
  40. 40.x + 3y = −1 and 2x + 4y = −4 →

Answer key

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

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