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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 520 · 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. 1.7x + 5y = −21 and 5x + 7y = −39 →
  2. 2.6x + 6y = 18 and 2x + 5y = 0 →
  3. 3.x + y = 6 and 4x + 5y = 27 →
  4. 4.5x + 9y = 89 and 9x + 5y = 93 →
  5. 5.3x + 4y = 22 and 5x + 5y = 30 →
  6. 6.4x + 2y = 18 and 2x + 4y = 12 →
  7. 7.6x − 2y = 28 and 4x − 5y = 15 →
  8. 8.4x + 2y = 28 and x − 5y = −37 →
  9. 9.2x − 5y = 27 and 2x − y = 7 →
  10. 10.3x + 6y = −21 and 3x + 2y = −1 →
  11. 11.9x + 5y = 96 and 5x + 9y = 72 →
  12. 12.x + 9y = 11 and 9x + y = −61 →
  13. 13.5x − 6y = 2 and x − 4y = −8 →
  14. 14.5x − 4y = −57 and 5x − 5y = −60 →
  15. 15.2x + 2y = −26 and x − 5y = 11 →
  16. 16.3x + 6y = 60 and 6x + 2y = 40 →
  17. 17.4x + 3y = 3 and x + 3y = 12 →
  18. 18.4x − 2y = 14 and 6x − y = 3 →
  19. 19.2x + 5y = 37 and 3x − 4y = −2 →
  20. 20.5x + 3y = −4 and 2x − 4y = 40 →
  21. 21.5x − y = −3 and 2x + 5y = −39 →
  22. 22.3x + y = −7 and x + 3y = 11 →
  23. 23.3x + 5y = −1 and 5x + 3y = 9 →
  24. 24.6x − 2y = 54 and 2x − y = 21 →
  25. 25.3x + 4y = −35 and 3x + 6y = −45 →
  26. 26.2x + 5y = 34 and 5x + y = 16 →
  27. 27.6x − y = 28 and 2x + 4y = 18 →
  28. 28.x + 5y = 51 and 3x − y = 9 →
  29. 29.5x + y = 33 and x + 3y = 15 →
  30. 30.4x + 2y = −22 and 2x + 4y = −2 →
  31. 31.x − 2y = −3 and 2x − 3y = −8 →
  32. 32.3x + 4y = −5 and 4x + 3y = −9 →
  33. 33.5x + 3y = −38 and 6x + 4y = −48 →
  34. 34.6x + y = −3 and x + 6y = 17 →
  35. 35.6x − 5y = −18 and 3x + 5y = −54 →
  36. 36.2x + 2y = −24 and 4x + 2y = −30 →
  37. 37.4x + 4y = −12 and x + 4y = −15 →
  38. 38.6x + 5y = 11 and 6x − y = 5 →
  39. 39.4x − 6y = 30 and 6x + 4y = 32 →
  40. 40.2x − 3y = 7 and 2x − 6y = 4 →

Answer key

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

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