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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 859 · 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 + 6y = 9 and 4x + 2y = 6 →
  2. 2.2x + 6y = 34 and 5x − 5y = 25 →
  3. 3.x − 3y = 8 and 4x + 2y = 4 →
  4. 4.4x + 5y = −23 and 5x + 4y = −13 →
  5. 5.9x + y = 57 and x + 9y = 33 →
  6. 6.3x + 2y = 3 and 2x + 4y = −22 →
  7. 7.5x + 2y = 39 and 2x + 5y = 45 →
  8. 8.x + y = 11 and 4x − 2y = 26 →
  9. 9.5x + 9y = 53 and 9x + 5y = 73 →
  10. 10.8x + y = 68 and x + 8y = 40 →
  11. 11.4x + y = −23 and 3x − 3y = −21 →
  12. 12.x − 2y = 3 and x + y = 9 →
  13. 13.5x + 4y = 12 and 5x − 4y = 68 →
  14. 14.6x − 4y = −80 and 5x + 5y = 0 →
  15. 15.x + 8y = −31 and 8x + y = 4 →
  16. 16.x − 5y = 6 and 3x + 3y = 0 →
  17. 17.x + 3y = 5 and 4x − 3y = 5 →
  18. 18.3x + 5y = 13 and 3x + 2y = 7 →
  19. 19.4x + 2y = −2 and 2x + 4y = 14 →
  20. 20.6x − y = −22 and x + y = 1 →
  21. 21.8x + y = −9 and x + 8y = 54 →
  22. 22.x + 2y = 15 and 6x − 2y = 20 →
  23. 23.6x + 4y = 38 and 4x − 2y = 2 →
  24. 24.x + 4y = 7 and 4x + 5y = 17 →
  25. 25.6x + 7y = 26 and 7x + 6y = 26 →
  26. 26.4x + 4y = 48 and 2x + 3y = 33 →
  27. 27.6x − 4y = 38 and x − 4y = −7 →
  28. 28.x + 6y = 12 and 4x + 5y = 29 →
  29. 29.9x + 7y = 78 and 7x + 9y = 82 →
  30. 30.2x + 2y = 12 and x + 4y = 9 →
  31. 31.6x + 4y = −4 and x + 3y = 18 →
  32. 32.6x + 5y = −27 and x + 3y = 2 →
  33. 33.3x + 6y = −45 and 3x − 4y = −5 →
  34. 34.4x + 5y = −23 and 5x + 4y = −31 →
  35. 35.7x + 6y = −56 and 6x + 7y = −61 →
  36. 36.9x + 5y = −37 and 5x + 9y = 23 →
  37. 37.x − 2y = 14 and 2x + y = −2 →
  38. 38.6x + 5y = 56 and 6x − 6y = 12 →
  39. 39.3x + 3y = −30 and x − 4y = 15 →
  40. 40.8x + y = 23 and x + 8y = −68 →

Answer key

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

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