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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 502 · 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 = −12 and 3x − 4y = 15 →
  2. 2.4x + 2y = −50 and 4x − 3y = −5 →
  3. 3.5x − 6y = −23 and 2x + 3y = 34 →
  4. 4.5x + 8y = −11 and 8x + 5y = −2 →
  5. 5.6x + 5y = 13 and 3x − 2y = −16 →
  6. 6.6x − 4y = 8 and 2x − 5y = −12 →
  7. 7.5x + 4y = 34 and 4x + 5y = 38 →
  8. 8.7x + 4y = 44 and 4x + 7y = 11 →
  9. 9.6x − 5y = 28 and x − 6y = 15 →
  10. 10.3x − 2y = −8 and 5x + y = −9 →
  11. 11.9x + y = −24 and x + 9y = −56 →
  12. 12.6x + 5y = −35 and x + 3y = −8 →
  13. 13.6x + 4y = −34 and 2x + 2y = −8 →
  14. 14.4x − 6y = −38 and 5x + 6y = 74 →
  15. 15.5x + 5y = 10 and 6x + 2y = 24 →
  16. 16.5x + 2y = 48 and 2x − 2y = −6 →
  17. 17.6x + y = −18 and 6x + 6y = −48 →
  18. 18.6x + 8y = 56 and 8x + 6y = 70 →
  19. 19.4x + 6y = 26 and 6x + 4y = 14 →
  20. 20.3x + y = 19 and x + 3y = 17 →
  21. 21.2x + y = −18 and x + 2y = −12 →
  22. 22.6x − 3y = −15 and 4x + 3y = 35 →
  23. 23.3x + 3y = 36 and 4x + y = 21 →
  24. 24.3x + y = 20 and 6x − 4y = −8 →
  25. 25.2x − 3y = 13 and 5x + 4y = 44 →
  26. 26.6x + 5y = −6 and 6x − 2y = −48 →
  27. 27.x + 4y = 25 and 6x + y = −11 →
  28. 28.x + 2y = 22 and 6x + 4y = 60 →
  29. 29.3x + 3y = −30 and x + 4y = −28 →
  30. 30.2x − 3y = 19 and x + 3y = −31 →
  31. 31.4x + 2y = −44 and 2x + 4y = −40 →
  32. 32.2x + 3y = 32 and 3x + 2y = 28 →
  33. 33.6x + 5y = 78 and 2x + y = 22 →
  34. 34.3x + 9y = 39 and 9x + 3y = 69 →
  35. 35.x + 6y = 29 and 6x + y = 34 →
  36. 36.2x + y = 15 and x + 2y = 21 →
  37. 37.2x + y = 5 and 4x + 4y = 12 →
  38. 38.x + 4y = 13 and 6x − y = −22 →
  39. 39.2x + 2y = −22 and x + 2y = −13 →
  40. 40.5x − 5y = −20 and x + y = −6 →

Answer key

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

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