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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 314 · 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 = 56 and 3x + 2y = 32 →
  2. 2.5x + 4y = 3 and 4x + 5y = −12 →
  3. 3.2x + y = 2 and 5x + y = 14 →
  4. 4.3x + 5y = 51 and 5x + 3y = 53 →
  5. 5.9x + 3y = 36 and 3x + 9y = 60 →
  6. 6.2x + 5y = 27 and 6x + 6y = 36 →
  7. 7.4x + y = −30 and x + 4y = 15 →
  8. 8.x − 2y = 3 and x − y = 5 →
  9. 9.3x + y = 18 and 3x − 2y = 0 →
  10. 10.5x + 6y = 33 and 5x − 6y = −63 →
  11. 11.x + 4y = 20 and x − 3y = −8 →
  12. 12.6x + 2y = 46 and x + 2y = 21 →
  13. 13.4x − 4y = 28 and x + 5y = 19 →
  14. 14.x + 4y = 32 and 4x + y = 23 →
  15. 15.x − 3y = −1 and 4x − 2y = 6 →
  16. 16.2x + 7y = 63 and 7x + 2y = 63 →
  17. 17.4x + 5y = −6 and 5x + 4y = −21 →
  18. 18.2x + 3y = 0 and 3x + 2y = 5 →
  19. 19.8x + 6y = 82 and 6x + 8y = 72 →
  20. 20.6x + 3y = −15 and 6x + 2y = −18 →
  21. 21.x + y = −9 and x + 6y = −49 →
  22. 22.5x + 5y = 30 and 5x − y = 6 →
  23. 23.4x − 5y = −15 and 6x + 2y = 44 →
  24. 24.4x + 2y = 28 and x − y = 10 →
  25. 25.4x − 2y = −44 and 5x + 2y = −19 →
  26. 26.3x + 9y = 3 and 9x + 3y = 57 →
  27. 27.x + 6y = 41 and 6x + y = 36 →
  28. 28.4x + 8y = −76 and 8x + 4y = −68 →
  29. 29.4x + y = −17 and x + 4y = −38 →
  30. 30.5x + 6y = 31 and 6x + 5y = 35 →
  31. 31.4x + 7y = 32 and 7x + 4y = 23 →
  32. 32.2x + y = 10 and 4x − 3y = 60 →
  33. 33.6x + 4y = −8 and 2x − 5y = 29 →
  34. 34.8x + 3y = 57 and 3x + 8y = −13 →
  35. 35.2x + y = 23 and x − 6y = −47 →
  36. 36.4x + 7y = 37 and 7x + 4y = 40 →
  37. 37.3x − 4y = −14 and 4x + 3y = −2 →
  38. 38.x − 2y = 16 and 4x − 6y = 52 →
  39. 39.5x − y = 42 and 4x − 4y = 24 →
  40. 40.6x + 5y = 2 and 4x + 4y = 0 →

Answer key

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

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