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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 591 · 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. 1.5x + 4y = 8 and 4x + 5y = 19 →
  2. 2.4x + 2y = −18 and x + 4y = 13 →
  3. 3.2x + 9y = −12 and 9x + 2y = 23 →
  4. 4.4x + y = 40 and x + 2y = 17 →
  5. 5.5x + y = −37 and 2x + 4y = −40 →
  6. 6.6x + y = −40 and x + 6y = −30 →
  7. 7.5x + 5y = 10 and 4x − 3y = 43 →
  8. 8.6x + 5y = −2 and 2x + 6y = 34 →
  9. 9.x − y = −12 and 4x − 5y = −55 →
  10. 10.x + 6y = 57 and x − 2y = −15 →
  11. 11.5x + 3y = 28 and 5x − 6y = 19 →
  12. 12.6x + 8y = 40 and 8x + 6y = 16 →
  13. 13.6x + y = −15 and x + 6y = −20 →
  14. 14.5x + 6y = 69 and 6x + 5y = 63 →
  15. 15.x − 6y = −26 and 3x − y = 7 →
  16. 16.x − y = −2 and 2x − y = −3 →
  17. 17.5x − 5y = −50 and 6x − 5y = −58 →
  18. 18.8x + 5y = −22 and 5x + 8y = −4 →
  19. 19.4x + 5y = 32 and 2x + 3y = 18 →
  20. 20.6x + 5y = −4 and 5x + 6y = −7 →
  21. 21.6x + 3y = 60 and 2x + 2y = 24 →
  22. 22.3x + 6y = 18 and x + 4y = 8 →
  23. 23.4x + 2y = 14 and 4x + 5y = 5 →
  24. 24.x + 4y = 2 and 3x − 5y = 23 →
  25. 25.4x − y = 1 and 6x − 5y = 19 →
  26. 26.x − y = −8 and x − 5y = −36 →
  27. 27.2x − 4y = 20 and 4x − 4y = 24 →
  28. 28.x + 2y = 2 and 2x + y = 13 →
  29. 29.7x + y = −50 and x + 7y = 34 →
  30. 30.4x + 6y = −8 and x − y = −12 →
  31. 31.x + 4y = −2 and 2x − 6y = 24 →
  32. 32.4x − 6y = −6 and x + 4y = 37 →
  33. 33.6x + 3y = 27 and 3x + 6y = 0 →
  34. 34.6x + 4y = 26 and 4x − 4y = 24 →
  35. 35.2x + 3y = 36 and 4x + 3y = 48 →
  36. 36.x + 2y = −5 and 2x + y = −16 →
  37. 37.2x + y = 9 and x + 2y = 6 →
  38. 38.4x + 3y = 51 and 4x + y = 41 →
  39. 39.3x + 2y = 43 and 6x + y = 62 →
  40. 40.9x + 8y = 51 and 8x + 9y = 51 →

Answer key

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

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