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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 151 · 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 + 2y = 13 and x − y = −11 →
  2. 2.7x + 4y = −11 and 4x + 7y = −44 →
  3. 3.5x − 3y = 28 and x + 3y = 2 →
  4. 4.4x + 3y = 40 and 2x − 5y = −6 →
  5. 5.2x + 4y = 34 and 4x + 2y = 20 →
  6. 6.5x + 5y = −5 and 2x + 5y = −20 →
  7. 7.6x − 6y = −48 and x + 6y = 27 →
  8. 8.3x + 4y = 51 and 4x + 3y = 54 →
  9. 9.2x + 3y = 23 and x − 2y = −6 →
  10. 10.4x − 6y = −34 and 2x + 3y = 13 →
  11. 11.6x + 4y = 12 and 4x + 6y = 38 →
  12. 12.2x + 7y = 60 and 7x + 2y = 30 →
  13. 13.3x + 5y = 26 and 5x + 3y = 22 →
  14. 14.x + 3y = 13 and x − y = 5 →
  15. 15.x + 6y = 33 and 2x + 3y = 12 →
  16. 16.x + 2y = −1 and 2x + y = 1 →
  17. 17.2x + 6y = 8 and 6x + 2y = 8 →
  18. 18.6x + y = 32 and 2x + 4y = 40 →
  19. 19.3x + y = −19 and x + 3y = −25 →
  20. 20.4x + 2y = 36 and 5x − y = 17 →
  21. 21.2x + 6y = 32 and 4x − 6y = −62 →
  22. 22.3x − 3y = 18 and 2x − 5y = 9 →
  23. 23.9x + 6y = 15 and 6x + 9y = 0 →
  24. 24.2x + 5y = −42 and 5x + 2y = −21 →
  25. 25.4x + 6y = −14 and 6x + 4y = −16 →
  26. 26.7x + y = 26 and x + 7y = 38 →
  27. 27.2x + 2y = −8 and 3x + y = 0 →
  28. 28.8x + 4y = 44 and 4x + 8y = 16 →
  29. 29.8x + 4y = 72 and 4x + 8y = 72 →
  30. 30.4x + 4y = 20 and 3x − y = 7 →
  31. 31.6x + 2y = 12 and 2x + 6y = −44 →
  32. 32.3x + 6y = 33 and 6x + 3y = 39 →
  33. 33.6x + 4y = −56 and x + y = −12 →
  34. 34.3x + 2y = 10 and 2x + 3y = 10 →
  35. 35.9x + y = 22 and x + 9y = 38 →
  36. 36.2x − 4y = 10 and 2x + 5y = 28 →
  37. 37.2x − 4y = −32 and 4x + y = −19 →
  38. 38.2x + 2y = −4 and 6x + 5y = −14 →
  39. 39.x − 5y = −44 and 5x − 6y = −49 →
  40. 40.5x + 3y = 13 and 3x + 5y = 11 →

Answer key

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

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