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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 809 · 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 − y = −2 and 6x − 4y = −12 →
  2. 2.7x + 2y = 44 and 2x + 7y = 19 →
  3. 3.5x − 4y = 23 and 5x + 3y = −26 →
  4. 4.3x + 9y = 54 and 9x + 3y = −6 →
  5. 5.x − y = −6 and 4x + 2y = −42 →
  6. 6.3x + 8y = 21 and 8x + 3y = −54 →
  7. 7.6x − 3y = −27 and 6x − 4y = −24 →
  8. 8.5x + 4y = 27 and 5x + 5y = 30 →
  9. 9.3x + 7y = −62 and 7x + 3y = −38 →
  10. 10.3x + 5y = 54 and x + 4y = 39 →
  11. 11.8x + 4y = 84 and 4x + 8y = 96 →
  12. 12.2x + y = 1 and x + 2y = −4 →
  13. 13.6x + 3y = 21 and 3x + 6y = −30 →
  14. 14.6x + 5y = −37 and 2x − 6y = −20 →
  15. 15.4x + 2y = 2 and x + 4y = 11 →
  16. 16.3x + 3y = −6 and 2x + 5y = −28 →
  17. 17.7x + 2y = 23 and 2x + 7y = 13 →
  18. 18.2x + 2y = 16 and 5x + 6y = 44 →
  19. 19.x − 2y = 12 and 5x + 6y = −20 →
  20. 20.6x − 6y = −54 and 4x − 5y = −43 →
  21. 21.x + 4y = −24 and 5x + 6y = −50 →
  22. 22.3x − y = −2 and 6x − 4y = −14 →
  23. 23.2x − 2y = 10 and 2x + y = −2 →
  24. 24.9x + y = 16 and x + 9y = 64 →
  25. 25.6x − 5y = −61 and 5x + y = −25 →
  26. 26.8x + 2y = 66 and 2x + 8y = 84 →
  27. 27.2x + 3y = 23 and 5x + 2y = 41 →
  28. 28.x + 6y = 14 and 2x − 6y = −8 →
  29. 29.x + 3y = 10 and 4x + 5y = 26 →
  30. 30.4x + 9y = −60 and 9x + 4y = −5 →
  31. 31.8x + y = 61 and x + 8y = −16 →
  32. 32.x + 2y = 10 and 2x + y = 14 →
  33. 33.2x + 3y = −23 and 3x + 2y = −17 →
  34. 34.2x − 3y = −12 and 3x + 4y = 50 →
  35. 35.3x + 6y = 15 and 2x − 2y = −14 →
  36. 36.5x + y = −19 and 6x − 4y = −28 →
  37. 37.2x + 3y = 29 and 3x + 2y = 26 →
  38. 38.5x + 2y = 40 and 4x + 4y = 44 →
  39. 39.6x + 5y = 22 and 5x + 5y = 20 →
  40. 40.x + 4y = 26 and 4x + y = 14 →

Answer key

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

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