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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 881 · 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. 1.2x + y = 13 and 2x − 4y = 8 →
  2. 2.9x + 2y = 66 and 2x + 9y = −11 →
  3. 3.8x + 2y = 68 and 2x + 8y = 2 →
  4. 4.6x + 2y = 16 and 2x + 2y = 8 →
  5. 5.4x + y = 5 and 2x + 3y = 5 →
  6. 6.2x + 9y = −25 and 9x + 2y = 3 →
  7. 7.x − 2y = 5 and 6x + 4y = 46 →
  8. 8.4x + 5y = 38 and x + 6y = 38 →
  9. 9.x + 2y = 6 and 2x − y = −8 →
  10. 10.5x + 4y = 38 and 5x + 3y = 31 →
  11. 11.4x + y = −16 and x + 4y = −34 →
  12. 12.2x + 4y = 36 and 4x + 4y = 40 →
  13. 13.8x + 3y = 62 and 3x + 8y = 37 →
  14. 14.6x + 9y = 33 and 9x + 6y = −18 →
  15. 15.6x − 6y = 78 and 3x − y = 31 →
  16. 16.3x + 4y = 18 and 5x + y = 13 →
  17. 17.3x + 2y = 33 and 2x + 3y = 32 →
  18. 18.2x + 6y = 14 and 6x + 2y = 26 →
  19. 19.x + 2y = −6 and 2x + 5y = −19 →
  20. 20.7x + 6y = 93 and 6x + 7y = 89 →
  21. 21.4x − 2y = 44 and 2x + 2y = 4 →
  22. 22.4x + 9y = −51 and 9x + 4y = −1 →
  23. 23.3x + y = −12 and x + 6y = 30 →
  24. 24.6x + 3y = −21 and 3x + 6y = −6 →
  25. 25.4x + 2y = 30 and 6x − y = 33 →
  26. 26.9x + 7y = −51 and 7x + 9y = −29 →
  27. 27.5x + 2y = 14 and 2x + 5y = −7 →
  28. 28.2x + 4y = 34 and 5x + 4y = 49 →
  29. 29.4x − 3y = 26 and 6x − 4y = 40 →
  30. 30.2x + y = 5 and x + 2y = −11 →
  31. 31.2x + 9y = 32 and 9x + 2y = −10 →
  32. 32.5x + 5y = −45 and 6x + 2y = −42 →
  33. 33.7x + 6y = −36 and 6x + 7y = −29 →
  34. 34.2x + 4y = −20 and 4x + 2y = −4 →
  35. 35.2x − 6y = −66 and 5x − 6y = −93 →
  36. 36.2x + 3y = 37 and 3x + 2y = 33 →
  37. 37.x + 3y = 18 and 4x + y = 28 →
  38. 38.2x − 3y = 19 and x − y = 8 →
  39. 39.4x − 5y = 26 and 5x + 5y = 55 →
  40. 40.x + 6y = 30 and 2x − 2y = 4 →

Answer key

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

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