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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 357 · 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 = −18 and 2x + 4y = −20 →
  2. 2.2x − 2y = −6 and x + 2y = −6 →
  3. 3.4x + y = 29 and 3x − y = 34 →
  4. 4.4x − 6y = −24 and 2x + 2y = 28 →
  5. 5.5x + 2y = −4 and 2x + 5y = −31 →
  6. 6.4x + y = −3 and x + 4y = 18 →
  7. 7.x + y = 5 and x + 5y = 1 →
  8. 8.4x + y = 10 and 2x − 4y = 14 →
  9. 9.x + 2y = 4 and 2x + y = 14 →
  10. 10.4x + 3y = 35 and x + 2y = 10 →
  11. 11.6x + 6y = −24 and 6x + 2y = 12 →
  12. 12.x + y = 13 and 6x + 3y = 63 →
  13. 13.5x − 6y = −38 and 3x − 3y = −18 →
  14. 14.x + y = −11 and 5x + y = −23 →
  15. 15.3x + 4y = 33 and 2x − 3y = −12 →
  16. 16.x + 6y = 26 and 4x + 2y = 38 →
  17. 17.x + 3y = −23 and 2x + y = −11 →
  18. 18.4x + 5y = 34 and 5x − y = −1 →
  19. 19.8x + 5y = 36 and 5x + 8y = 42 →
  20. 20.5x − 6y = 7 and 2x + 2y = −6 →
  21. 21.7x + 2y = −17 and 2x + 7y = 8 →
  22. 22.2x − 3y = −7 and 3x + 3y = 42 →
  23. 23.2x + 3y = 8 and 3x + 2y = −3 →
  24. 24.6x + 3y = 9 and 4x − y = 21 →
  25. 25.x + 4y = 31 and x + 5y = 37 →
  26. 26.6x + 7y = 103 and 7x + 6y = 105 →
  27. 27.6x + y = −29 and x − 3y = 11 →
  28. 28.x + 2y = 9 and 3x + 2y = 11 →
  29. 29.5x − y = −39 and 3x + 6y = 3 →
  30. 30.5x + y = 30 and 2x + y = 9 →
  31. 31.x − 4y = 21 and 4x + 4y = −56 →
  32. 32.4x − y = 25 and 5x + y = 47 →
  33. 33.2x + 6y = 42 and 5x − y = −39 →
  34. 34.9x + 5y = 22 and 5x + 9y = 6 →
  35. 35.x + 3y = −2 and x + 6y = −5 →
  36. 36.5x − y = 13 and 3x + 4y = 40 →
  37. 37.2x + 7y = −57 and 7x + 2y = 3 →
  38. 38.x − 4y = 19 and 5x − 2y = −13 →
  39. 39.4x − 3y = −17 and 2x − 6y = −40 →
  40. 40.9x + 7y = 95 and 7x + 9y = 81 →

Answer key

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

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