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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 232 · 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. 1.3x + 5y = −17 and 6x + 2y = −50 →
  2. 2.4x + y = −10 and x + 4y = −25 →
  3. 3.4x − 4y = 68 and 4x + y = 23 →
  4. 4.x + 4y = −10 and 5x − 5y = −25 →
  5. 5.5x + y = −23 and 2x + 2y = −6 →
  6. 6.x − 2y = −11 and x + 2y = 5 →
  7. 7.4x − 2y = −28 and x + y = 5 →
  8. 8.x + 8y = 67 and 8x + y = 32 →
  9. 9.6x + 8y = 8 and 8x + 6y = −22 →
  10. 10.x + 5y = 7 and 3x − 2y = 4 →
  11. 11.4x − 6y = 48 and x + 5y = −14 →
  12. 12.5x + 4y = −47 and 5x + 5y = −55 →
  13. 13.3x + y = 24 and x + 3y = 32 →
  14. 14.4x + 5y = 31 and 5x + 4y = 23 →
  15. 15.x + 5y = 8 and 5x + y = −8 →
  16. 16.x − 5y = 41 and 2x + y = −6 →
  17. 17.3x + 4y = 10 and x − 6y = 18 →
  18. 18.x + 5y = −22 and x + 4y = −17 →
  19. 19.7x + 9y = −73 and 9x + 7y = −71 →
  20. 20.3x − 5y = 11 and 6x − 5y = 17 →
  21. 21.5x + 2y = 14 and 2x + 5y = 14 →
  22. 22.2x + y = −8 and x + 2y = −10 →
  23. 23.8x + y = 71 and x + 8y = 64 →
  24. 24.3x + 6y = 0 and 5x − 5y = −45 →
  25. 25.6x − 5y = 7 and 2x − 2y = 2 →
  26. 26.5x + 6y = −1 and 6x + 4y = 2 →
  27. 27.4x + 8y = 56 and 8x + 4y = 40 →
  28. 28.9x + 6y = 84 and 6x + 9y = 66 →
  29. 29.4x + 8y = 8 and 8x + 4y = 40 →
  30. 30.2x + 9y = 2 and 9x + 2y = −68 →
  31. 31.2x + 2y = 6 and 6x + 2y = 38 →
  32. 32.3x + y = 19 and 3x + 3y = 33 →
  33. 33.5x + 3y = −23 and x − 3y = 17 →
  34. 34.5x + y = 31 and 5x + 6y = −14 →
  35. 35.x + 3y = 19 and 3x + y = 1 →
  36. 36.3x − 5y = −26 and 5x − y = 8 →
  37. 37.5x + 2y = −22 and 3x + y = −14 →
  38. 38.x + 3y = 10 and 4x − 3y = 25 →
  39. 39.x + 5y = 35 and x − 3y = −13 →
  40. 40.x − 3y = −7 and 3x − 4y = −1 →

Answer key

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

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