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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 414 · 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.x + 3y = 9 and 2x + y = −7 →
  2. 2.9x + 5y = 33 and 5x + 9y = −19 →
  3. 3.3x − y = −3 and 6x + y = 12 →
  4. 4.3x + 4y = 34 and 2x + 2y = 20 →
  5. 5.x + 4y = −20 and x + 6y = −32 →
  6. 6.6x + 3y = 51 and 4x + y = 31 →
  7. 7.6x + 4y = −14 and 4x + 6y = −36 →
  8. 8.3x − 4y = −26 and 3x + 2y = 4 →
  9. 9.4x + 6y = −14 and 6x + 4y = 14 →
  10. 10.2x + 5y = 14 and 2x − y = 2 →
  11. 11.x + 7y = −58 and 7x + y = −22 →
  12. 12.2x + 4y = 20 and x − 4y = −44 →
  13. 13.5x + 3y = 8 and 3x + 5y = 8 →
  14. 14.5x + 6y = −32 and 5x + 5y = −30 →
  15. 15.3x + 2y = −22 and 2x + 3y = −28 →
  16. 16.4x + y = −5 and x + 4y = 10 →
  17. 17.6x + 5y = 29 and 5x − 6y = 14 →
  18. 18.2x + y = 22 and 2x + 3y = 38 →
  19. 19.5x + 2y = 3 and 5x + 5y = 0 →
  20. 20.x + 5y = 38 and x + 3y = 20 →
  21. 21.5x − y = −32 and 6x − 2y = −44 →
  22. 22.2x + 3y = 26 and 4x + 3y = 28 →
  23. 23.4x − 6y = 22 and 5x + y = 36 →
  24. 24.x − y = −2 and 6x − 4y = 2 →
  25. 25.3x + 2y = −9 and 2x + 3y = 4 →
  26. 26.2x + 9y = 99 and 9x + 2y = 99 →
  27. 27.4x − 2y = −6 and 2x − 4y = −18 →
  28. 28.8x + 4y = 60 and 4x + 8y = 84 →
  29. 29.x − 3y = 23 and 6x − 5y = 34 →
  30. 30.3x + 3y = 36 and 6x + y = 37 →
  31. 31.7x + 6y = 97 and 6x + 7y = 98 →
  32. 32.3x + 2y = 8 and 2x + 3y = 7 →
  33. 33.9x + 5y = 52 and 5x + 9y = 4 →
  34. 34.6x + 3y = 18 and 6x + 2y = 16 →
  35. 35.x − 6y = −14 and 3x − 2y = −10 →
  36. 36.2x + 4y = 20 and 4x + 2y = 28 →
  37. 37.6x + 3y = 42 and x − 2y = 2 →
  38. 38.x + 7y = −15 and 7x + y = −57 →
  39. 39.8x + 4y = −56 and 4x + 8y = −64 →
  40. 40.8x + y = 25 and x + 8y = 11 →

Answer key

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

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