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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 191 · 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 = 8 and 5x − 3y = 14 →
  2. 2.6x − 5y = −17 and x + 5y = 38 →
  3. 3.7x + 6y = 3 and 6x + 7y = 10 →
  4. 4.3x − y = 14 and 6x − 4y = 14 →
  5. 5.3x − 6y = −33 and 3x + 3y = 21 →
  6. 6.6x + y = −23 and x − y = −5 →
  7. 7.2x + y = −2 and x + 2y = −13 →
  8. 8.x + y = −2 and 4x + 2y = 2 →
  9. 9.6x + 2y = 24 and 2x + 6y = −8 →
  10. 10.4x − y = −33 and 5x + 3y = −37 →
  11. 11.2x − 5y = 46 and 5x + 5y = −25 →
  12. 12.6x + y = 25 and x + 6y = 10 →
  13. 13.8x + 7y = 65 and 7x + 8y = 70 →
  14. 14.6x + 5y = 17 and 4x − y = −19 →
  15. 15.2x + y = 4 and 6x − 3y = 0 →
  16. 16.8x + 3y = 55 and 3x + 8y = 0 →
  17. 17.6x + 4y = 58 and 4x + 6y = 42 →
  18. 18.x + 3y = −1 and 3x + y = 13 →
  19. 19.x − y = −5 and 6x + 2y = 2 →
  20. 20.x + 8y = −22 and 8x + y = −50 →
  21. 21.5x + 5y = 5 and 2x − y = 23 →
  22. 22.4x + 5y = 13 and 5x + 4y = 5 →
  23. 23.x + 4y = 31 and 4x + y = 34 →
  24. 24.5x + 2y = −36 and 2x + 5y = −6 →
  25. 25.5x + 2y = 33 and x + 6y = 29 →
  26. 26.6x + y = 44 and 3x + 5y = 31 →
  27. 27.5x + y = 26 and x − 5y = 52 →
  28. 28.3x + 2y = 13 and 4x + y = 19 →
  29. 29.6x + 8y = −54 and 8x + 6y = −30 →
  30. 30.x + 6y = 7 and 6x + y = −28 →
  31. 31.x − y = 12 and x + 3y = −24 →
  32. 32.x − 3y = −26 and x + 3y = 22 →
  33. 33.4x − 2y = −40 and 4x + 2y = −24 →
  34. 34.6x + 3y = 15 and 2x + 3y = 3 →
  35. 35.4x − 3y = 20 and 3x − y = 10 →
  36. 36.7x + 2y = 61 and 2x + 7y = 11 →
  37. 37.7x + 6y = 10 and 6x + 7y = 16 →
  38. 38.6x − 2y = −34 and x + 3y = 21 →
  39. 39.9x + 8y = −43 and 8x + 9y = −42 →
  40. 40.3x + 9y = 30 and 9x + 3y = 66 →

Answer key

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

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