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Simultaneous Equations Worksheet

Vedic maths trick 34: Simultaneous equations · Set 80 · 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 + 6y = 33 and 2x + 3y = 21 →
  2. 2.4x − 2y = 16 and 5x + y = 34 →
  3. 3.6x + 7y = 13 and 7x + 6y = 13 →
  4. 4.3x + 3y = −3 and 5x + 6y = 1 →
  5. 5.5x + 4y = 34 and 4x + 5y = 38 →
  6. 6.8x + y = 19 and x + 8y = −37 →
  7. 7.2x − y = −12 and 6x − 4y = −38 →
  8. 8.7x + 2y = −8 and 2x + 7y = 17 →
  9. 9.8x + 4y = −48 and 4x + 8y = 12 →
  10. 10.6x − 6y = 18 and 6x − y = 23 →
  11. 11.4x − 4y = 4 and 3x + 2y = 38 →
  12. 12.x + 8y = 43 and 8x + y = 29 →
  13. 13.5x + y = 42 and 6x + 5y = 77 →
  14. 14.x + 2y = −25 and 6x + 3y = −78 →
  15. 15.6x − 6y = 6 and 4x + 5y = −68 →
  16. 16.5x + 3y = 7 and x + 6y = −31 →
  17. 17.3x + 2y = 1 and 4x − 5y = 9 →
  18. 18.2x + 4y = 38 and 3x + y = 17 →
  19. 19.x − 2y = −11 and x − y = −3 →
  20. 20.7x + 9y = 28 and 9x + 7y = 4 →
  21. 21.x + 2y = −12 and 6x + y = 27 →
  22. 22.4x + 6y = 60 and 6x + 4y = 70 →
  23. 23.5x − 3y = −9 and 5x − 5y = −25 →
  24. 24.8x + y = −47 and x + 8y = 2 →
  25. 25.9x + 5y = −8 and 5x + 9y = −48 →
  26. 26.2x + 3y = 10 and 2x + 6y = 16 →
  27. 27.6x + 4y = 16 and 4x − 6y = 54 →
  28. 28.x − 4y = 39 and x − 6y = 57 →
  29. 29.7x + y = 17 and x + 7y = 23 →
  30. 30.5x + 2y = −26 and 2x − 4y = 28 →
  31. 31.5x + 5y = 50 and x + 3y = 16 →
  32. 32.5x + 4y = −21 and 4x + 5y = −15 →
  33. 33.4x + 4y = 60 and 4x + 6y = 74 →
  34. 34.4x + 9y = −60 and 9x + 4y = −70 →
  35. 35.3x + y = −22 and 2x + 3y = −3 →
  36. 36.x − 3y = 29 and 3x − 2y = 38 →
  37. 37.4x + 6y = 30 and x + y = 6 →
  38. 38.3x + 5y = −2 and 5x + 3y = 2 →
  39. 39.5x + 2y = −32 and 2x + 5y = −38 →
  40. 40.2x + 3y = 16 and 3x + 2y = 19 →

Answer key

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

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