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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 92 · 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 + 9y = 46 and 9x + 2y = 53 →
  2. 2.x + 2y = 6 and 2x + y = 6 →
  3. 3.4x + 2y = 6 and 2x + 4y = 24 →
  4. 4.x − 3y = −20 and x − y = −8 →
  5. 5.7x + 8y = 38 and 8x + 7y = 37 →
  6. 6.6x + 2y = 4 and x + y = −2 →
  7. 7.4x − 2y = 12 and 6x + 5y = 50 →
  8. 8.7x + 6y = 55 and 6x + 7y = 49 →
  9. 9.6x + 9y = −24 and 9x + 6y = −6 →
  10. 10.x + 3y = 19 and 2x − 3y = −7 →
  11. 11.2x + 5y = −43 and 5x + 2y = −55 →
  12. 12.2x + 7y = 47 and 7x + 2y = 52 →
  13. 13.3x − 3y = 0 and x + 5y = 24 →
  14. 14.5x + 3y = 67 and x − 2y = −10 →
  15. 15.6x − 5y = 25 and 2x + 3y = 13 →
  16. 16.2x + 4y = 28 and 2x + 3y = 24 →
  17. 17.2x + y = −7 and 6x + 6y = −12 →
  18. 18.4x + 3y = −40 and 4x + 2y = −32 →
  19. 19.6x − 2y = 10 and x + 2y = −3 →
  20. 20.5x + y = 12 and x + 5y = 12 →
  21. 21.6x + 5y = 14 and x − 3y = 10 →
  22. 22.2x + 4y = 10 and x + 5y = 14 →
  23. 23.3x − 2y = 20 and x + 4y = 16 →
  24. 24.4x − 3y = −47 and 5x − 6y = −70 →
  25. 25.5x + y = 11 and x + 5y = 31 →
  26. 26.4x + 7y = 45 and 7x + 4y = 54 →
  27. 27.9x + y = 46 and x + 9y = −66 →
  28. 28.x + 2y = −2 and 2x − 2y = −10 →
  29. 29.2x − 3y = 41 and 2x + 4y = −22 →
  30. 30.2x + 3y = −22 and 3x + 4y = −31 →
  31. 31.5x + 6y = −67 and 5x + 2y = −39 →
  32. 32.3x + y = 20 and 4x − 3y = 18 →
  33. 33.x + 7y = 1 and 7x + y = 55 →
  34. 34.4x + 5y = −4 and 3x + 6y = −12 →
  35. 35.3x + 5y = 28 and 5x + 3y = 36 →
  36. 36.5x + 2y = 13 and 2x + 5y = 22 →
  37. 37.9x + 6y = 69 and 6x + 9y = 51 →
  38. 38.x − y = −3 and 4x + 3y = 37 →
  39. 39.8x + y = 54 and x + 8y = 54 →
  40. 40.2x − 2y = −4 and 2x + 3y = 1 →

Answer key

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

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