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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 318 · 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. 1.6x − y = 42 and 5x + y = 46 →
  2. 2.x + 3y = 25 and 3x + y = 3 →
  3. 3.6x + 4y = −6 and 4x + 3y = −5 →
  4. 4.3x + 2y = 43 and 2x + 3y = 42 →
  5. 5.4x + y = 11 and 5x − 6y = 79 →
  6. 6.3x + y = 14 and 3x − 2y = 8 →
  7. 7.5x + 4y = 37 and 2x + 2y = 18 →
  8. 8.3x + y = 14 and 2x + 3y = 14 →
  9. 9.2x − 2y = 8 and 6x − 3y = 21 →
  10. 10.5x + 2y = 46 and 2x + 5y = 31 →
  11. 11.6x − 6y = 24 and 3x + 3y = −24 →
  12. 12.5x + 4y = 22 and 4x + 5y = 23 →
  13. 13.6x − 3y = −27 and 5x − 2y = −23 →
  14. 14.5x + 2y = 28 and 2x + 4y = 8 →
  15. 15.2x + 4y = −36 and 6x + 3y = −63 →
  16. 16.3x + 8y = −46 and 8x + 3y = −31 →
  17. 17.8x + 9y = 136 and 9x + 8y = 136 →
  18. 18.5x − 5y = 65 and 5x − 2y = 38 →
  19. 19.5x + 4y = 31 and 2x + 2y = 16 →
  20. 20.4x − 5y = 14 and x + 6y = −11 →
  21. 21.4x + 2y = 34 and 3x + y = 25 →
  22. 22.5x + 2y = 17 and x + 2y = 5 →
  23. 23.4x + 6y = 14 and 6x + 6y = 18 →
  24. 24.6x + 2y = 52 and 2x + 6y = 28 →
  25. 25.x + 2y = 10 and 2x + 2y = 18 →
  26. 26.x − y = 11 and 2x + 2y = −6 →
  27. 27.9x + 5y = 86 and 5x + 9y = 54 →
  28. 28.2x − 5y = −24 and 5x − 2y = −39 →
  29. 29.3x + y = 25 and x + 2y = 20 →
  30. 30.4x + 7y = −45 and 7x + 4y = −21 →
  31. 31.3x − 4y = −26 and 3x + 4y = 38 →
  32. 32.x + 3y = −11 and 2x + 5y = −18 →
  33. 33.6x + y = 43 and x + 6y = 13 →
  34. 34.4x − 3y = 21 and x + 4y = −9 →
  35. 35.x + 2y = −1 and 2x + y = 10 →
  36. 36.5x − 6y = 46 and 4x + 2y = 30 →
  37. 37.3x + y = 8 and 4x − 5y = −2 →
  38. 38.6x + 2y = 20 and x + 3y = −2 →
  39. 39.x + 5y = 27 and 5x + 2y = 43 →
  40. 40.5x − 6y = 74 and x − 3y = 31 →

Answer key

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

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