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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 529 · 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. 1.5x + y = −17 and 4x + 5y = −22 →
  2. 2.2x − 6y = −14 and 6x + 3y = 63 →
  3. 3.x + 4y = −20 and 4x + y = 25 →
  4. 4.4x + 2y = 38 and 3x + 6y = 69 →
  5. 5.4x + 8y = −24 and 8x + 4y = −36 →
  6. 6.3x + 7y = 50 and 7x + 3y = 10 →
  7. 7.2x + 9y = 74 and 9x + 2y = 25 →
  8. 8.8x + 7y = −32 and 7x + 8y = −43 →
  9. 9.x + 3y = 24 and 5x + 4y = 43 →
  10. 10.3x + 5y = 18 and 6x − 6y = −12 →
  11. 11.3x + y = 8 and x + 3y = 0 →
  12. 12.4x − 2y = 30 and x + 3y = 4 →
  13. 13.4x − 6y = −64 and 6x + y = −36 →
  14. 14.2x + 4y = −26 and 4x + 2y = −22 →
  15. 15.3x + 4y = −48 and 4x + 5y = −61 →
  16. 16.4x + 7y = 26 and 7x + 4y = 29 →
  17. 17.4x + 3y = 29 and 3x + 3y = 24 →
  18. 18.6x + 2y = 8 and 4x + 5y = −24 →
  19. 19.6x + y = 14 and 2x − 5y = −38 →
  20. 20.x + 5y = −11 and 3x − 2y = −16 →
  21. 21.3x + 2y = 40 and 4x + y = 40 →
  22. 22.8x + 2y = 34 and 2x + 8y = 46 →
  23. 23.3x + 9y = 6 and 9x + 3y = −30 →
  24. 24.2x + y = 1 and x + 2y = 14 →
  25. 25.2x + 2y = −10 and 5x − y = −49 →
  26. 26.4x + 6y = −6 and 4x − y = −13 →
  27. 27.5x + 6y = −19 and 2x + 3y = −13 →
  28. 28.4x + y = −11 and x + 4y = 31 →
  29. 29.4x + y = 13 and 5x − 5y = −40 →
  30. 30.9x + 4y = 44 and 4x + 9y = 34 →
  31. 31.5x + y = 15 and 2x − 3y = 23 →
  32. 32.2x + 5y = 39 and 3x + 3y = 27 →
  33. 33.5x + 9y = 23 and 9x + 5y = 19 →
  34. 34.2x + 3y = −6 and 2x − 4y = 50 →
  35. 35.8x + 2y = 14 and 2x + 8y = 26 →
  36. 36.2x − 2y = 0 and x − 3y = −2 →
  37. 37.4x − 3y = 0 and 3x − 4y = −14 →
  38. 38.8x + 3y = 43 and 3x + 8y = 23 →
  39. 39.4x + 4y = 12 and x + 6y = −2 →
  40. 40.4x + y = −34 and x + 4y = −31 →

Answer key

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

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