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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 539 · 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. 1.4x + 4y = −12 and 2x + 4y = 4 →
  2. 2.6x + 6y = −36 and 5x − 5y = −40 →
  3. 3.4x + y = −36 and 5x + y = −43 →
  4. 4.4x − 5y = −17 and 3x + 3y = −6 →
  5. 5.2x + 6y = 22 and 6x + 2y = 2 →
  6. 6.7x + 8y = 33 and 8x + 7y = 27 →
  7. 7.8x + 6y = 10 and 6x + 8y = 32 →
  8. 8.x + 7y = 36 and 7x + y = 12 →
  9. 9.4x + 3y = 28 and 3x + y = 11 →
  10. 10.x + 3y = 30 and 3x − 6y = −45 →
  11. 11.4x + 9y = 48 and 9x + 4y = 43 →
  12. 12.x + 7y = 47 and 7x + y = 41 →
  13. 13.x + 3y = −23 and 6x − 5y = 0 →
  14. 14.6x + 2y = 66 and 4x − 4y = −4 →
  15. 15.4x + 6y = 34 and 4x + 2y = 14 →
  16. 16.6x + y = 3 and 5x − 6y = −59 →
  17. 17.3x + y = −8 and x + 3y = 0 →
  18. 18.6x − y = 25 and 3x + 3y = 9 →
  19. 19.5x + y = 22 and 5x − 2y = 46 →
  20. 20.3x + 9y = −69 and 9x + 3y = −15 →
  21. 21.2x − 4y = −20 and x + 5y = 32 →
  22. 22.3x + 6y = 81 and 3x + 5y = 72 →
  23. 23.2x + y = 5 and 4x − 5y = −53 →
  24. 24.9x + 2y = 39 and 2x + 9y = 60 →
  25. 25.2x − 5y = 4 and 5x + y = 37 →
  26. 26.4x + 4y = −48 and 5x − 6y = −5 →
  27. 27.3x + y = −31 and 6x + 3y = −66 →
  28. 28.3x + 7y = −44 and 7x + 3y = 4 →
  29. 29.5x + 6y = 9 and 2x + 2y = 4 →
  30. 30.x + 3y = 23 and 3x + y = 29 →
  31. 31.9x + 6y = −21 and 6x + 9y = −39 →
  32. 32.9x + 8y = 62 and 8x + 9y = 57 →
  33. 33.5x + 4y = 15 and 3x − 2y = −13 →
  34. 34.6x − 2y = −62 and 4x − 5y = −56 →
  35. 35.4x − 4y = 0 and 4x + 3y = 28 →
  36. 36.x − 3y = −11 and x + 6y = 34 →
  37. 37.6x + 9y = 45 and 9x + 6y = 45 →
  38. 38.x + 2y = 8 and 4x + 4y = 12 →
  39. 39.2x + 5y = −3 and 6x + 2y = 4 →
  40. 40.4x + 6y = −34 and x + 5y = −33 →

Answer key

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

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