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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 56 · 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. 1.4x − 3y = 41 and 6x + y = 23 →
  2. 2.3x + 5y = −19 and 6x − 3y = 66 →
  3. 3.6x + 4y = −46 and x + 5y = −38 →
  4. 4.2x + 3y = 17 and 3x − 3y = −12 →
  5. 5.3x + y = 20 and 2x − 2y = −8 →
  6. 6.2x + 4y = −2 and 3x − 6y = −15 →
  7. 7.5x + 3y = 4 and 3x + 5y = 28 →
  8. 8.4x + 5y = 32 and 3x + y = 13 →
  9. 9.4x + 3y = 42 and 2x + 2y = 22 →
  10. 10.2x + 3y = 7 and 3x + 2y = −7 →
  11. 11.3x + 9y = 75 and 9x + 3y = 57 →
  12. 12.3x + 2y = 15 and 2x + 3y = 5 →
  13. 13.x + 4y = 31 and 3x + y = 16 →
  14. 14.5x + y = −6 and 4x + 3y = 4 →
  15. 15.3x + 4y = 4 and x + y = 3 →
  16. 16.x + y = −3 and 4x + 2y = 2 →
  17. 17.x − 3y = 26 and 3x − 2y = 22 →
  18. 18.4x + 3y = 1 and 3x + 4y = 6 →
  19. 19.x + 2y = −5 and 2x + y = 11 →
  20. 20.5x + 2y = 12 and x + y = 3 →
  21. 21.x − 2y = −14 and 5x − y = −16 →
  22. 22.6x + 2y = −24 and 2x − 6y = −48 →
  23. 23.2x + 5y = −12 and 6x + 3y = 36 →
  24. 24.x − 4y = −28 and 4x + 2y = 32 →
  25. 25.x + 4y = 31 and 4x + y = 4 →
  26. 26.6x + 5y = 99 and 5x + 6y = 99 →
  27. 27.4x + 2y = 38 and 5x + y = 37 →
  28. 28.2x + 4y = 38 and 4x + 2y = 40 →
  29. 29.3x + 2y = −25 and 2x + 3y = −15 →
  30. 30.3x + 2y = 6 and 2x + 3y = 14 →
  31. 31.5x + y = −29 and x + 5y = 23 →
  32. 32.2x − 2y = 2 and 6x + 5y = 72 →
  33. 33.2x + 7y = −15 and 7x + 2y = −30 →
  34. 34.x + 5y = 37 and 2x − 3y = −4 →
  35. 35.3x + 5y = 13 and 5x − 4y = −3 →
  36. 36.2x + 8y = −44 and 8x + 2y = 4 →
  37. 37.8x + 9y = 7 and 9x + 8y = −7 →
  38. 38.2x + 8y = 58 and 8x + 2y = −8 →
  39. 39.8x + 4y = −12 and 4x + 8y = 36 →
  40. 40.6x − 4y = −32 and 6x + y = −7 →

Answer key

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

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