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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 928 · 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 + 5y = −4 and 3x + 6y = 6 →
  2. 2.2x + y = −12 and x + 2y = −12 →
  3. 3.6x + 3y = 33 and 3x + 6y = 39 →
  4. 4.7x + y = −61 and x + 7y = 5 →
  5. 5.x + 3y = 19 and x + y = 5 →
  6. 6.8x + 3y = −14 and 3x + 8y = 36 →
  7. 7.2x + 7y = −66 and 7x + 2y = −51 →
  8. 8.2x + 3y = 33 and x + 6y = 39 →
  9. 9.x + 2y = 7 and x + y = 4 →
  10. 10.2x + 6y = 28 and 6x + 2y = 4 →
  11. 11.9x + 3y = 33 and 3x + 9y = 27 →
  12. 12.x + y = 5 and 2x + 3y = 11 →
  13. 13.4x + 3y = 23 and x + 2y = 17 →
  14. 14.7x + 5y = −14 and 5x + 7y = −34 →
  15. 15.4x − 3y = −27 and 3x − 3y = −21 →
  16. 16.8x + 6y = −30 and 6x + 8y = −54 →
  17. 17.x + 4y = −2 and 4x + y = −23 →
  18. 18.6x + 2y = 58 and 4x + y = 36 →
  19. 19.4x + 3y = −13 and x − 5y = 37 →
  20. 20.9x + 7y = 36 and 7x + 9y = 60 →
  21. 21.6x − 3y = 36 and 4x + 3y = 4 →
  22. 22.6x + 8y = −2 and 8x + 6y = 16 →
  23. 23.x + 5y = 7 and 6x − 2y = −54 →
  24. 24.2x + 4y = 34 and 4x + 2y = 44 →
  25. 25.2x − 2y = 8 and x + 3y = −20 →
  26. 26.9x + 7y = −34 and 7x + 9y = −30 →
  27. 27.5x + 3y = −24 and 3x + 5y = −8 →
  28. 28.6x + 3y = 0 and x − 5y = 11 →
  29. 29.3x + 9y = 42 and 9x + 3y = 54 →
  30. 30.6x + 3y = −27 and x − 4y = −36 →
  31. 31.4x − 3y = 6 and 6x + 6y = 72 →
  32. 32.2x + 5y = 14 and 6x + 2y = 16 →
  33. 33.x + 2y = 22 and 6x + 2y = 52 →
  34. 34.3x + 5y = 39 and 6x + 4y = 24 →
  35. 35.5x + 6y = −55 and 6x + 4y = −50 →
  36. 36.6x + 2y = 26 and 2x + 5y = 13 →
  37. 37.3x + 6y = 27 and 6x + 3y = −9 →
  38. 38.7x + 6y = 43 and 6x + 7y = 35 →
  39. 39.7x + 5y = −9 and 5x + 7y = 21 →
  40. 40.x − 6y = 11 and x + 3y = −16 →

Answer key

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

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