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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 641 · 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. 1.9x + 3y = 36 and 3x + 9y = 84 →
  2. 2.5x + 2y = 47 and x + y = 10 →
  3. 3.5x + y = 24 and x + 5y = 0 →
  4. 4.3x − 5y = −35 and 2x − y = −14 →
  5. 5.x − 2y = 5 and x + 3y = 0 →
  6. 6.4x + y = 13 and x + 4y = −23 →
  7. 7.3x − 3y = 0 and 4x − 6y = −4 →
  8. 8.x − 6y = −33 and 5x + y = 21 →
  9. 9.2x + 5y = 51 and 5x + 2y = 54 →
  10. 10.x − 4y = −30 and 2x + 6y = 52 →
  11. 11.4x + 5y = 20 and 4x + 2y = −4 →
  12. 12.2x + 6y = −30 and 4x − 2y = −4 →
  13. 13.3x + 6y = 18 and x + 6y = 2 →
  14. 14.3x + 4y = 5 and 5x + 2y = −29 →
  15. 15.x + 6y = 49 and 2x + 5y = 35 →
  16. 16.3x + y = 17 and 2x − 5y = −34 →
  17. 17.x + 3y = 20 and 3x + y = 12 →
  18. 18.x − y = −2 and 2x − 5y = −31 →
  19. 19.5x + 3y = −21 and 3x + 5y = −3 →
  20. 20.5x + 3y = 34 and 2x + y = 12 →
  21. 21.7x + 3y = 46 and 3x + 7y = 14 →
  22. 22.x + 5y = 25 and 2x + 2y = 18 →
  23. 23.4x + 8y = 24 and 8x + 4y = 36 →
  24. 24.2x + 7y = 45 and 7x + 2y = 45 →
  25. 25.4x + 4y = −24 and x − 5y = 36 →
  26. 26.6x + 7y = −3 and 7x + 6y = 3 →
  27. 27.6x − 2y = 28 and 4x − 5y = 48 →
  28. 28.x − 2y = 13 and 4x + 5y = −52 →
  29. 29.4x + 2y = 22 and 3x − 3y = 30 →
  30. 30.7x + 4y = 43 and 4x + 7y = 34 →
  31. 31.2x + 8y = −32 and 8x + 2y = 22 →
  32. 32.x + 6y = −10 and 2x + y = 13 →
  33. 33.3x − 2y = −1 and x − 3y = −5 →
  34. 34.5x + y = −7 and 2x − y = −14 →
  35. 35.6x + 4y = −40 and 4x + 6y = −30 →
  36. 36.2x + 3y = 28 and x − 3y = −22 →
  37. 37.3x + 4y = 6 and 4x + 3y = −6 →
  38. 38.4x + 8y = 24 and 8x + 4y = 24 →
  39. 39.x + 2y = 10 and 2x + 3y = 13 →
  40. 40.2x + 5y = 48 and x − y = 3 →

Answer key

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

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