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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 130 · 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 + 2y = 23 and 2x + 3y = 12 →
  2. 2.7x + 2y = −55 and 2x + 7y = 10 →
  3. 3.4x + 5y = −33 and 5x + 4y = −39 →
  4. 4.3x + 3y = 6 and 5x + 4y = 13 →
  5. 5.6x + 9y = 75 and 9x + 6y = 75 →
  6. 6.3x + y = 16 and 6x + 3y = 33 →
  7. 7.x − 2y = 25 and 2x + 5y = −22 →
  8. 8.4x + 7y = 1 and 7x + 4y = 10 →
  9. 9.x + 3y = −25 and 5x + y = −13 →
  10. 10.x − y = −10 and 6x + 4y = 0 →
  11. 11.2x + 3y = 38 and 3x + 2y = 37 →
  12. 12.2x − 3y = −7 and x − y = 0 →
  13. 13.2x + 5y = 33 and 5x − 6y = −10 →
  14. 14.6x + 5y = 28 and 3x − y = 7 →
  15. 15.4x + 5y = −44 and 5x − 6y = −6 →
  16. 16.3x + y = 17 and 3x + 5y = 49 →
  17. 17.3x − y = 17 and 4x + 5y = 48 →
  18. 18.9x + y = −40 and x + 9y = −40 →
  19. 19.3x + 3y = 39 and 5x − 5y = −5 →
  20. 20.4x + 5y = −60 and 5x − 5y = 15 →
  21. 21.x − 6y = 27 and 5x + 3y = 3 →
  22. 22.5x + 2y = 14 and x + 4y = −8 →
  23. 23.3x − 5y = 69 and 5x + 4y = 4 →
  24. 24.4x + 3y = 16 and 3x + 5y = 23 →
  25. 25.3x + 6y = 45 and 6x − 4y = −54 →
  26. 26.5x + 6y = 27 and 6x + 2y = 22 →
  27. 27.3x + 4y = 27 and x + 6y = 37 →
  28. 28.3x + 3y = 6 and 6x − 2y = −60 →
  29. 29.4x + 7y = −73 and 7x + 4y = −70 →
  30. 30.2x − 2y = 4 and x − 4y = 26 →
  31. 31.6x − 4y = 66 and x − 6y = 27 →
  32. 32.7x + y = 29 and x + 7y = 59 →
  33. 33.2x + y = 13 and 2x + 6y = 18 →
  34. 34.3x − 5y = −9 and 3x + 2y = 33 →
  35. 35.x + 4y = −24 and 2x − y = −12 →
  36. 36.2x + 4y = 6 and 2x + y = −12 →
  37. 37.6x − 6y = −102 and 4x + y = −23 →
  38. 38.2x + 6y = 24 and 3x + 5y = 24 →
  39. 39.8x + 2y = 8 and 2x + 8y = −28 →
  40. 40.8x + 6y = −34 and 6x + 8y = −36 →

Answer key

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

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