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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 184 · 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.x + y = 4 and x − 3y = −24 →
  2. 2.6x + 3y = 9 and 6x − 5y = 1 →
  3. 3.x + y = 14 and 4x + 3y = 50 →
  4. 4.x + 5y = 23 and 5x + 2y = 46 →
  5. 5.6x + 2y = 36 and x + y = 2 →
  6. 6.6x − 2y = −36 and 5x + 6y = 16 →
  7. 7.5x − 6y = −64 and 2x − y = −20 →
  8. 8.6x − y = −46 and x + y = −3 →
  9. 9.5x + 6y = −6 and 6x + 5y = 6 →
  10. 10.3x + y = −11 and x + 5y = 1 →
  11. 11.2x + 4y = 34 and 4x + y = 33 →
  12. 12.5x + 5y = −25 and 4x + 6y = −36 →
  13. 13.4x + 5y = 15 and 5x + 4y = 3 →
  14. 14.4x − 3y = 29 and x − y = 9 →
  15. 15.9x + 4y = 61 and 4x + 9y = 56 →
  16. 16.3x + 6y = 27 and 6x + 3y = 18 →
  17. 17.4x + 6y = 20 and x − 2y = 12 →
  18. 18.3x + 4y = 6 and 5x + 6y = 12 →
  19. 19.2x + y = −1 and 2x − 4y = 34 →
  20. 20.5x + 3y = 54 and 3x − 5y = −22 →
  21. 21.x + y = −2 and 4x + 5y = −15 →
  22. 22.2x + 5y = 23 and 4x − 4y = 32 →
  23. 23.7x + 2y = 40 and 2x + 7y = 50 →
  24. 24.4x − 5y = −9 and 5x − 5y = −5 →
  25. 25.5x + 3y = 32 and 3x + 5y = 48 →
  26. 26.2x + 3y = −2 and 4x − 6y = 44 →
  27. 27.6x + 5y = 16 and 5x + 6y = 28 →
  28. 28.6x + 9y = −24 and 9x + 6y = 9 →
  29. 29.6x + 3y = 27 and 2x − 6y = 72 →
  30. 30.6x + 2y = 14 and 6x + 4y = 16 →
  31. 31.2x + y = 24 and x + 2y = 21 →
  32. 32.6x + 3y = −39 and 3x + 6y = −60 →
  33. 33.6x + 4y = 12 and 2x + 6y = 32 →
  34. 34.4x − 4y = −4 and 2x + 3y = −32 →
  35. 35.x + 2y = 18 and 2x + 6y = 52 →
  36. 36.x − 6y = −33 and 2x + 2y = 18 →
  37. 37.6x + 8y = −14 and 8x + 6y = −14 →
  38. 38.6x + 6y = −6 and x − 2y = 5 →
  39. 39.6x + 3y = 21 and 4x − 2y = 2 →
  40. 40.9x + y = 62 and x + 9y = −2 →

Answer key

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

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