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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 813 · 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 + 4y = −30 and 4x + y = −15 →
  2. 2.5x − 5y = 45 and 2x + 5y = −10 →
  3. 3.6x + y = −3 and 6x + 2y = −12 →
  4. 4.3x + 6y = 66 and 6x + 3y = 69 →
  5. 5.5x + 4y = −3 and 4x + 2y = −12 →
  6. 6.6x + 2y = −24 and x − y = −12 →
  7. 7.8x + 6y = 6 and 6x + 8y = −6 →
  8. 8.x + 6y = 17 and 6x + y = −38 →
  9. 9.8x + 3y = 34 and 3x + 8y = −1 →
  10. 10.7x + 5y = 108 and 5x + 7y = 108 →
  11. 11.6x + 7y = 51 and 7x + 6y = 40 →
  12. 12.4x + 6y = −28 and 3x − 6y = 63 →
  13. 13.2x + 5y = −36 and x − 2y = 0 →
  14. 14.5x + 2y = 29 and 4x + y = 19 →
  15. 15.2x + 5y = 54 and 5x + 2y = 51 →
  16. 16.x − 2y = 11 and 6x − 3y = 39 →
  17. 17.x − 3y = −15 and 6x + 3y = −27 →
  18. 18.2x + 6y = −16 and 5x + 5y = 10 →
  19. 19.8x + 9y = 97 and 9x + 8y = 90 →
  20. 20.6x + 6y = −30 and 6x − 3y = 24 →
  21. 21.3x + y = −4 and 4x + 6y = 4 →
  22. 22.3x + 5y = −19 and 5x + 3y = 11 →
  23. 23.x + 5y = 2 and 2x + 3y = −3 →
  24. 24.6x − y = 10 and 6x + 4y = 50 →
  25. 25.2x + 5y = 2 and 5x + 2y = −16 →
  26. 26.x + 2y = 18 and 3x − 3y = 9 →
  27. 27.x + 3y = 33 and 3x + y = 27 →
  28. 28.4x + 3y = −57 and 3x + 5y = −62 →
  29. 29.9x + 6y = 33 and 6x + 9y = 57 →
  30. 30.6x + 3y = 36 and 5x − 3y = 63 →
  31. 31.6x − 5y = −6 and 3x + 6y = −54 →
  32. 32.3x − 4y = −25 and 4x + 6y = 12 →
  33. 33.x + y = 4 and 4x + y = 22 →
  34. 34.2x + y = −3 and 4x − 3y = −21 →
  35. 35.5x + 5y = −85 and 5x + 4y = −76 →
  36. 36.9x + 7y = 62 and 7x + 9y = 66 →
  37. 37.3x + 5y = −18 and 5x + 3y = −14 →
  38. 38.6x + 4y = 22 and 3x − 2y = 31 →
  39. 39.3x − 3y = 39 and 2x + 5y = −2 →
  40. 40.6x + 2y = −4 and x − 4y = −5 →

Answer key

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

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