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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 517 · 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 = −9 and 5x + 6y = 3 →
  2. 2.4x − y = 29 and 5x + 5y = 55 →
  3. 3.x + 9y = 32 and 9x + y = 48 →
  4. 4.3x + 4y = 2 and 4x + 3y = −9 →
  5. 5.x + 4y = 27 and 4x + y = −12 →
  6. 6.3x − 3y = 9 and 2x + 2y = 14 →
  7. 7.5x − y = −24 and 6x − 3y = −36 →
  8. 8.9x + 2y = 76 and 2x + 9y = 34 →
  9. 9.4x + y = 21 and x + 4y = 24 →
  10. 10.4x + 2y = 36 and 4x − y = 24 →
  11. 11.3x − y = 19 and 3x + 6y = 33 →
  12. 12.x − 2y = 11 and 2x + 6y = −28 →
  13. 13.4x + y = −5 and x + 5y = 32 →
  14. 14.5x + 2y = 13 and 3x + 2y = 7 →
  15. 15.x + 6y = −15 and 2x + 4y = −22 →
  16. 16.6x + 4y = −16 and 4x + 6y = −14 →
  17. 17.3x + 2y = −37 and x + 3y = −24 →
  18. 18.5x + 2y = 31 and 2x + 4y = 38 →
  19. 19.4x + 5y = −34 and x + 2y = −10 →
  20. 20.5x + 6y = 83 and 4x + 3y = 52 →
  21. 21.6x − y = 36 and 3x + 2y = 33 →
  22. 22.4x + 6y = 38 and 6x + 4y = 22 →
  23. 23.6x + 3y = 33 and 3x + 6y = 3 →
  24. 24.x + 3y = 19 and 6x + 3y = 54 →
  25. 25.3x + 2y = 35 and 3x + 4y = 43 →
  26. 26.6x + y = 2 and x + y = 7 →
  27. 27.x + y = 8 and 6x + 4y = 36 →
  28. 28.3x − 2y = 24 and 4x − 6y = 42 →
  29. 29.3x − 2y = 39 and 6x + 2y = 24 →
  30. 30.2x − 5y = −28 and 6x + 6y = 42 →
  31. 31.8x + 6y = 26 and 6x + 8y = 30 →
  32. 32.x + 2y = 12 and 2x − 6y = −26 →
  33. 33.5x + y = 43 and 2x − y = 6 →
  34. 34.3x + 8y = 28 and 8x + 3y = 38 →
  35. 35.3x − 3y = −30 and 5x + 4y = −32 →
  36. 36.2x + 9y = 38 and 9x + 2y = −60 →
  37. 37.8x + 6y = 36 and 6x + 8y = 34 →
  38. 38.2x − 6y = −42 and x + 5y = 43 →
  39. 39.x − 4y = 17 and 3x + 6y = −21 →
  40. 40.x + 2y = 5 and 5x + 3y = 11 →

Answer key

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

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