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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 462 · 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. 1.4x + 6y = 14 and 6x + 4y = 36 →
  2. 2.3x + 2y = −4 and 2x + 3y = −16 →
  3. 3.4x + y = 11 and x + 4y = 14 →
  4. 4.x + 2y = 18 and x − 4y = −18 →
  5. 5.5x + 2y = 7 and 2x + 5y = 7 →
  6. 6.5x + y = 43 and 2x + 4y = 10 →
  7. 7.2x + y = 15 and x + 2y = 12 →
  8. 8.2x + 4y = −10 and 2x + y = 2 →
  9. 9.x + 3y = 14 and 2x + y = 13 →
  10. 10.9x + 2y = 34 and 2x + 9y = 76 →
  11. 11.x + 8y = 10 and 8x + y = 17 →
  12. 12.5x + 2y = 59 and 2x + 5y = 53 →
  13. 13.2x + 3y = 18 and 2x + 4y = 26 →
  14. 14.x + y = 0 and 5x + y = −32 →
  15. 15.2x − 5y = −1 and x + 6y = −9 →
  16. 16.x − y = −5 and 5x + y = −43 →
  17. 17.9x + 5y = 11 and 5x + 9y = −25 →
  18. 18.5x + 3y = −5 and 5x + 6y = 10 →
  19. 19.5x − 6y = −4 and 2x − 3y = −4 →
  20. 20.4x − 3y = 22 and 2x + 5y = −2 →
  21. 21.3x − y = 33 and x − 2y = 26 →
  22. 22.3x + 8y = 75 and 8x + 3y = 90 →
  23. 23.4x + 6y = 2 and 3x − 3y = 9 →
  24. 24.4x + 7y = −15 and 7x + 4y = −18 →
  25. 25.x − 2y = −13 and 6x + y = 26 →
  26. 26.4x + 2y = 6 and 2x + 6y = 38 →
  27. 27.x − 5y = −27 and 5x + y = −31 →
  28. 28.2x + 3y = 20 and x + 3y = 19 →
  29. 29.4x + 6y = −12 and 4x + 5y = −14 →
  30. 30.4x + 7y = 36 and 7x + 4y = −3 →
  31. 31.8x + y = 19 and x + 8y = 26 →
  32. 32.6x + 5y = 22 and x + 3y = 21 →
  33. 33.2x + 3y = −7 and 4x + 2y = −10 →
  34. 34.4x + 2y = −18 and 4x + 5y = −15 →
  35. 35.x + 2y = −5 and 6x − y = −56 →
  36. 36.5x + 9y = −9 and 9x + 5y = 51 →
  37. 37.4x − 4y = −4 and 3x − 2y = 3 →
  38. 38.2x − y = 6 and x + 3y = 17 →
  39. 39.5x + 6y = 57 and 4x + 2y = 40 →
  40. 40.6x + 3y = −48 and 3x + 6y = −15 →

Answer key

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

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